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2026-01-01
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2026-02-28
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<p>124 Learners</p>
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<p>INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta</p>
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<p>Last updated on<strong>September 24, 2025</strong></p>
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<p>INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034</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 645 and 180.</p>
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<p>SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)</p>
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<h2>What is the GCF of 645 and 180?</h2>
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<p>USA - 251, Little Falls Drive, Wilmington, Delaware 19808</p>
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<p>The<a>greatest common factor</a><a>of</a>645 and 180 is 15. 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>VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City</p>
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<p>The GCF of two numbers cannot be negative because divisors are always positive.</p>
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<p>VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam</p>
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<h2>How to find the GCF of 645 and 180?</h2>
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<p>UAE - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates</p>
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<p>To find the GCF of 645 and 180, a few methods are described below</p>
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<p>UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom</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 / by Euclidean Algorithm</li>
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</ul><h2>GCF of 645 and 180 by Using Listing of Factors</h2>
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<p>Steps to find the GCF of 645 and 180 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 645 = 1, 3, 5, 15, 43, 129, 215, 645.</p>
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<p>Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.</p>
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<p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 645 and 180: 1, 3, 5, 15.</p>
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<p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 15.</p>
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<p>The GCF of 645 and 180 is 15.</p>
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<h3>Explore Our Programs</h3>
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<p>No Courses Available</p>
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<h2>GCF of 645 and 180 Using Prime Factorization</h2>
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<p>To find the GCF of 645 and 180 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 645: 645 = 3 x 5 x 43</p>
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<p>Prime Factors of 180: 180 = 2 x 2 x 3 x 3 x 5</p>
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<p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factors are: 3 x 5</p>
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<p><strong>Step 3:</strong>Multiply the common prime factors 3 x 5 = 15.</p>
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<p>The Greatest Common Factor of 645 and 180 is 15.</p>
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<h2>GCF of 645 and 180 Using Division Method or Euclidean Algorithm Method</h2>
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<p>Find the GCF of 645 and 180 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>
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<p>Step 1: First, divide the larger number by the smaller number</p>
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<p>Here, divide 645 by 180 645 ÷ 180 = 3 (<a>quotient</a>),</p>
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<p>The<a>remainder</a>is calculated as 645 - (180×3) = 105</p>
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<p>The remainder is 105, not zero, so continue the process</p>
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<p><strong>Step 2:</strong>Now divide the previous divisor (180) by the previous remainder (105)</p>
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<p>Divide 180 by 105 180 ÷ 105 = 1 (quotient), remainder = 180 - (105×1) = 75</p>
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<p><strong>Step 3:</strong>Divide the previous divisor (105) by the previous remainder (75)</p>
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<p>Divide 105 by 75 105 ÷ 75 = 1 (quotient), remainder = 105 - (75×1) = 30</p>
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<p><strong>Step 4:</strong>Divide the previous divisor (75) by the previous remainder (30) 75 ÷ 30 = 2 (quotient), remainder = 75 - (30×2) = 15</p>
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<p><strong>Step 5:</strong>Divide the previous divisor (30) by the previous remainder (15) 30 ÷ 15 = 2 (quotient), remainder = 30 - (15×2) = 0 The remainder is zero, the divisor will become the GCF.</p>
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<p>The GCF of 645 and 180 is 15.</p>
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<h2>Common Mistakes and How to Avoid Them in GCF of 645 and 180</h2>
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<p>Finding GCF of 645 and 180 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 gardener has 645 tulip bulbs and 180 daffodil bulbs. She wants to plant them in equal sections, with the largest number of bulbs in each section. How many bulbs will be in each section?</p>
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<p>Okay, lets begin</p>
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<p>We should find the GCF of 645 and 180 GCF of 645 and 180 3 x 5 = 15.</p>
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<p>There are 15 equal sections 645 ÷ 15 = 43 180 ÷ 15 = 12</p>
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<p>There will be 15 sections, and each section gets 43 tulip bulbs and 12 daffodil bulbs.</p>
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<h3>Explanation</h3>
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<p>As the GCF of 645 and 180 is 15, the gardener can make 15 sections.</p>
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<p>Now divide 645 and 180 by 15.</p>
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<p>Each section gets 43 tulip bulbs and 12 daffodil bulbs.</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<p>A shipping company has 645 large boxes and 180 small boxes. They want to arrange them in stacks with the same number of boxes in each stack, using the largest possible number of boxes per stack. How many boxes will be in each stack?</p>
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<p>Okay, lets begin</p>
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<p>GCF of 645 and 180 3 x 5 = 15.</p>
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<p>So each stack will have 15 boxes.</p>
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<h3>Explanation</h3>
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<p>There are 645 large and 180 small boxes. To find the total number of boxes in each stack, we should find the GCF of 645 and 180. There will be 15 boxes in each stack.</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 645 meters of red fabric and 180 meters of blue fabric. She wants to cut both fabrics 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 645 and 180</p>
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<p>The GCF of 645 and 180 3 x 5 = 15.</p>
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<p>The fabric is 15 meters long.</p>
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<h3>Explanation</h3>
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<p>For calculating the longest length of the fabric, first, we need to calculate the GCF of 645 and 180 which is 15.</p>
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<p>The length of each piece of the fabric will be 15 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 645 cm long and the other 180 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 645 and 180 3 x 5 = 15.</p>
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<p>The longest length of each piece is 15 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, 645 cm and 180 cm, respectively.</p>
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<p>We have to find the GCF of 645 and 180, which is 15 cm.</p>
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<p>The longest length of each piece is 15 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 645 and ‘a’ is 15, and the LCM is 7740. Find ‘a’.</p>
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<p>Okay, lets begin</p>
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<p>The value of ‘a’ is 180.</p>
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<h3>Explanation</h3>
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<p>GCF x LCM = product of the numbers</p>
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<p>15 × 7740 = 645 × a</p>
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<p>116100 = 645a</p>
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<p>a = 116100 ÷ 645 = 180</p>
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<p>Well explained 👍</p>
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<h2>FAQs on the Greatest Common Factor of 645 and 180</h2>
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<h3>1.What is the LCM of 645 and 180?</h3>
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<p>The LCM of 645 and 180 is 7740.</p>
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<h3>2.Is 645 divisible by 5?</h3>
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<p>Yes, 645 is divisible by 5 because it ends in 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 180?</h3>
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<p>The prime factorization of 180 is 2 x 2 x 3 x 3 x 5.</p>
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<h3>5.Are 645 and 180 prime numbers?</h3>
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<p>No, 645 and 180 are not prime numbers because both of them have more than two factors.</p>
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<h2>Important Glossaries for GCF of 645 and 180</h2>
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<ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.</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, 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 45 are 3 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 13 is divided by 5, the remainder is 3 and the quotient is 2.</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 5 and 10 is 10.</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>