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Original
2026-01-01
Modified
2026-02-28
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<p>150 Learners</p>
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<p>Last updated on<strong>September 24, 2025</strong></p>
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<p>The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 625 and 1000.</p>
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<h2>What is the GCF of 625 and 1000?</h2>
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<p>The<a>greatest common factor</a>of 625 and 1000 is 125. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>
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<p>The GCF of two numbers cannot be negative because divisors are always positive.</p>
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<h2>How to find the GCF of 625 and 1000?</h2>
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<p>To find the GCF of 625 and 1000, a few methods are described below </p>
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<ul><li>Listing Factors </li>
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<li>Prime Factorization </li>
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<li>Long Division Method / Euclidean Algorithm</li>
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</ul><h2>GCF of 625 and 1000 by Using Listing of Factors</h2>
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<p>Steps to find the GCF of 625 and 1000 using the listing of<a>factors</a></p>
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<p><strong>Step 1:</strong>Firstly, list the factors of each number</p>
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<p>Factors of 625 = 1, 5, 25, 125, 625.</p>
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<p>Factors of 1000 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 625 and 1000: 1, 5, 25, 125.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 125.</p>
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<p>The GCF of 625 and 1000 is 125.</p>
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<h2>GCF of 625 and 1000 Using Prime Factorization</h2>
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<p>To find the GCF of 625 and 1000 using the Prime Factorization Method, follow these steps:</p>
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<p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>
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<p>Prime Factors of 625: 625 = 5 × 5 × 5 × 5 = 54</p>
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<p>Prime Factors of 1000: 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 23 × 53</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 5 × 5 × 5 = 53</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 53 = 125.</p>
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<p>The Greatest Common Factor of 625 and 1000 is 125.</p>
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<h2>GCF of 625 and 1000 Using Division Method or Euclidean Algorithm Method</h2>
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<p>Find the GCF of 625 and 1000 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Find the GCF of 625 and 1000 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>
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<p><strong>Step 1:</strong>First, divide the larger number by the smaller number</p>
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<p>Here, divide 1000 by 625 1000 ÷ 625 = 1 (<a>quotient</a>),</p>
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<p>Here, divide 1000 by 625 1000 ÷ 625 = 1 (<a>quotient</a>),</p>
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<p>The<a>remainder</a>is calculated as 1000 - (625×1) = 375</p>
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<p>The<a>remainder</a>is calculated as 1000 - (625×1) = 375</p>
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<p>The remainder is 375, not zero, so continue the process</p>
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<p>The remainder is 375, not zero, so continue the process</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (625) by the previous remainder (375)</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (625) by the previous remainder (375)</p>
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<p>Divide 625 by 375 625 ÷ 375 = 1 (quotient), remainder = 625 - (375×1) = 250</p>
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<p>Divide 625 by 375 625 ÷ 375 = 1 (quotient), remainder = 625 - (375×1) = 250</p>
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<p>The remainder is 250, not zero, so continue the process</p>
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<p>The remainder is 250, not zero, so continue the process</p>
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<p><strong>Step 3:</strong>Now divide the previous divisor (375) by the previous remainder (250)</p>
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<p><strong>Step 3:</strong>Now divide the previous divisor (375) by the previous remainder (250)</p>
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<p>Divide 375 by 250 375 ÷ 250 = 1 (quotient), remainder = 375 - (250×1) = 125</p>
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<p>Divide 375 by 250 375 ÷ 250 = 1 (quotient), remainder = 375 - (250×1) = 125</p>
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<p>The remainder is 125, not zero, so continue the process</p>
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<p>The remainder is 125, not zero, so continue the process</p>
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<p><strong>Step 4:</strong>Now divide the previous divisor (250) by the previous remainder (125)</p>
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<p><strong>Step 4:</strong>Now divide the previous divisor (250) by the previous remainder (125)</p>
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<p>Divide 250 by 125 250 ÷ 125 = 2 (quotient), remainder = 250 - (125×2) = 0</p>
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<p>Divide 250 by 125 250 ÷ 125 = 2 (quotient), remainder = 250 - (125×2) = 0</p>
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<p>The remainder is zero, the divisor will become the GCF.</p>
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<p>The remainder is zero, the divisor will become the GCF.</p>
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<p>The GCF of 625 and 1000 is 125.</p>
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<p>The GCF of 625 and 1000 is 125.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 625 and 1000</h2>
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<p>Finding GCF of 625 and 1000 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>
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<h3>Problem 1</h3>
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<p>A teacher has 625 pencils and 1000 erasers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?</p>
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<p>Okay, lets begin</p>
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<p>We should find the GCF of 625 and 1000 GCF of 625 and 1000 53 = 125.</p>
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<p>There are 125 equal groups 625 ÷ 125 = 5 1000 ÷ 125 = 8</p>
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<p>There will be 125 groups, and each group gets 5 pencils and 8 erasers.</p>
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<h3>Explanation</h3>
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<p>As the GCF of 625 and 1000 is 125, the teacher can make 125 groups.</p>
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<p>Now divide 625 and 1000 by 125.</p>
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<p>Each group gets 5 pencils and 8 erasers.</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>A school has 625 red chairs and 1000 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?</p>
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<p>Okay, lets begin</p>
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<p>GCF of 625 and 1000 53 = 125.</p>
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<p>So each row will have 125 chairs.</p>
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<h3>Explanation</h3>
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<p>There are 625 red and 1000 blue chairs.</p>
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<p>To find the total number of chairs in each row, we should find the GCF of 625 and 1000.</p>
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<p>There will be 125 chairs in each row.</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<p>A tailor has 625 meters of red ribbon and 1000 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?</p>
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<p>Okay, lets begin</p>
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<p>For calculating the longest equal length, we have to calculate the GCF of 625 and 1000</p>
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<p>The GCF of 625 and 1000 53 = 125.</p>
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<p>The ribbon is 125 meters long.</p>
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<h3>Explanation</h3>
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<p>For calculating the longest length of the ribbon first we need to calculate the GCF of 625 and 1000 which is 125.</p>
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<p>The length of each piece of the ribbon will be 125 meters.</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<p>A carpenter has two wooden planks, one 625 cm long and the other 1000 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?</p>
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<p>Okay, lets begin</p>
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<p>The carpenter needs the longest piece of wood GCF of 625 and 1000 53 = 125.</p>
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<p>The longest length of each piece is 125 cm.</p>
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<h3>Explanation</h3>
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<p>To find the longest length of each piece of the two wooden planks, 625 cm and 1000 cm, respectively.</p>
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<p>We have to find the GCF of 625 and 1000, which is 125 cm.</p>
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<p>The longest length of each piece is 125 cm.</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<p>If the GCF of 625 and ‘a’ is 125, and the LCM is 5000. Find ‘a’.</p>
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<p>Okay, lets begin</p>
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<p>The value of ‘a’ is 1000.</p>
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<h3>Explanation</h3>
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<p>GCF × LCM = product of the numbers</p>
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<p>125 × 5000 = 625 × a</p>
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<p>625000 = 625a</p>
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<p>a = 625000 ÷ 625 = 1000</p>
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<p>Well explained 👍</p>
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<h2>FAQs on the Greatest Common Factor of 625 and 1000</h2>
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<h3>1.What is the LCM of 625 and 1000?</h3>
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<p>The LCM of 625 and 1000 is 5000.</p>
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<h3>2.Is 625 divisible by 5?</h3>
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<p>Yes, 625 is divisible by 5 because it ends in a 5.</p>
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<h3>3.What will be the GCF of any two prime numbers?</h3>
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<p>The common factor of<a>prime numbers</a>is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.</p>
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<h3>4.What is the prime factorization of 1000?</h3>
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<p>The prime factorization of 1000 is 23 × 53.</p>
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<h3>5.Are 625 and 1000 prime numbers?</h3>
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<p>No, 625 and 1000 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 625 and 1000</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 125 are 1, 5, 25, and 125.</li>
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</ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on.</li>
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</ul><ul><li><strong>Prime Factors:</strong>These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 1000 are 2 and 5.</li>
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</ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 1000 is divided by 625, the remainder is 375 and the quotient is 1.</li>
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</ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 625 and 1000 is 5000.</li>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h3>About the Author</h3>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<h3>Fun Fact</h3>
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<p>: She loves to read number jokes and games.</p>