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2 <p>Last updated on<strong>August 14, 2025</strong></p>

3 <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 3 and 20.</p>

4 <h2>What is the GCF of 3 and 20?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>3 and 20 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the number.</p>

6 <p>If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.</p>

7 <h2>How to find the GCF of 3 and 20?</h2>

8 <p>To find the GCF of 3 and 20, a few methods are described below -</p>

9 <ol><li>Listing Factors</li>

10 <li>Prime Factorization</li>

11 <li>Long Division Method / by Euclidean Algorithm</li>

12 </ol><h2>GCF of 3 and 20 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 3 and 20 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number Factors of 3 = 1, 3. Factors of 20 = 1, 2, 4, 5, 10, 20.</p>

15 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factors of 3 and 20: 1.</p>

16 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that both numbers have is 1. The GCF of 3 and 20 is 1.</p>

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19 <h2>GCF of 3 and 20 Using Prime Factorization</h2>

18 <h2>GCF of 3 and 20 Using Prime Factorization</h2>

20 <p>To find the GCF of 3 and 20 using the Prime Factorization Method, follow these steps:</p>

19 <p>To find the GCF of 3 and 20 using the Prime Factorization Method, follow these steps:</p>

21 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 3: 3 = 3 Prime Factors of 20: 20 = 2 x 2 x 5 = 2² x 5</p>

20 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number Prime Factors of 3: 3 = 3 Prime Factors of 20: 20 = 2 x 2 x 5 = 2² x 5</p>

22 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 1 (since there are no common prime factors other than 1)</p>

21 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: 1 (since there are no common prime factors other than 1)</p>

23 <p><strong>Step 3:</strong>Multiply the common prime factors The Greatest Common Factor of 3 and 20 is 1.</p>

22 <p><strong>Step 3:</strong>Multiply the common prime factors The Greatest Common Factor of 3 and 20 is 1.</p>

24 <h2>GCF of 3 and 20 Using Division Method or Euclidean Algorithm Method</h2>

23 <h2>GCF of 3 and 20 Using Division Method or Euclidean Algorithm Method</h2>

25 <p>Find the GCF of 3 and 20 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

24 <p>Find the GCF of 3 and 20 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

26 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 20 by 3 20 ÷ 3 = 6 (<a>quotient</a>), The<a>remainder</a>is calculated as 20 - (3×6) = 2 The remainder is 2, not zero, so continue the process</p>

25 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number Here, divide 20 by 3 20 ÷ 3 = 6 (<a>quotient</a>), The<a>remainder</a>is calculated as 20 - (3×6) = 2 The remainder is 2, not zero, so continue the process</p>

27 <p><strong>Step 2:</strong>Now divide the previous divisor (3) by the previous remainder (2) Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 - (2×1) = 1 The remainder is 1, not zero, so continue the process</p>

26 <p><strong>Step 2:</strong>Now divide the previous divisor (3) by the previous remainder (2) Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 - (2×1) = 1 The remainder is 1, not zero, so continue the process</p>

28 <p><strong>Step 3:</strong>Now divide the previous divisor (2) by the previous remainder (1) Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 - (1×2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 3 and 20 is 1.</p>

27 <p><strong>Step 3:</strong>Now divide the previous divisor (2) by the previous remainder (1) Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 - (1×2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 3 and 20 is 1.</p>

29 <h2>Common Mistakes and How to Avoid Them in GCF of 3 and 20</h2>

28 <h2>Common Mistakes and How to Avoid Them in GCF of 3 and 20</h2>

30 <p>Finding GCF of 3 and 20 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

29 <p>Finding GCF of 3 and 20 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>A teacher has 3 apples and 20 bananas. 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>

31 <p>A teacher has 3 apples and 20 bananas. 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>

33 <p>Okay, lets begin</p>

32 <p>Okay, lets begin</p>

34 <p>We should find GCF of 3 and 20 GCF of 3 and 20 is 1.</p>

33 <p>We should find GCF of 3 and 20 GCF of 3 and 20 is 1.</p>

35 <p>There are 1 equal groups 3 ÷ 1 = 3 20 ÷ 1 = 20</p>

34 <p>There are 1 equal groups 3 ÷ 1 = 3 20 ÷ 1 = 20</p>

36 <p>There will be 1 group, and each group gets 3 apples and 20 bananas.</p>

35 <p>There will be 1 group, and each group gets 3 apples and 20 bananas.</p>

37 <h3>Explanation</h3>

36 <h3>Explanation</h3>

38 <p>As the GCF of 3 and 20 is 1, the teacher can make only 1 group. Now divide 3 and 20 by 1. Each group gets 3 apples and 20 bananas.</p>

37 <p>As the GCF of 3 and 20 is 1, the teacher can make only 1 group. Now divide 3 and 20 by 1. Each group gets 3 apples and 20 bananas.</p>

39 <p>Well explained 👍</p>

38 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

39 <h3>Problem 2</h3>

41 <p>A school has 3 red chairs and 20 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>

40 <p>A school has 3 red chairs and 20 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>

42 <p>Okay, lets begin</p>

41 <p>Okay, lets begin</p>

43 <p>GCF of 3 and 20 is 1. So each row will have 1 chair.</p>

42 <p>GCF of 3 and 20 is 1. So each row will have 1 chair.</p>

44 <h3>Explanation</h3>

43 <h3>Explanation</h3>

45 <p>There are 3 red and 20 blue chairs. To find the total number of chairs in each row, we should find the GCF of 3 and 20. There will be 1 chair in each row.</p>

44 <p>There are 3 red and 20 blue chairs. To find the total number of chairs in each row, we should find the GCF of 3 and 20. There will be 1 chair in each row.</p>

46 <p>Well explained 👍</p>

45 <p>Well explained 👍</p>

47 <h3>Problem 3</h3>

46 <h3>Problem 3</h3>

48 <p>A tailor has 3 meters of red ribbon and 20 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>

47 <p>A tailor has 3 meters of red ribbon and 20 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>

49 <p>Okay, lets begin</p>

48 <p>Okay, lets begin</p>

50 <p>For calculating longest equal length, we have to calculate the GCF of 3 and 20 The GCF of 3 and 20 is 1. The ribbon is 1 meter long.</p>

49 <p>For calculating longest equal length, we have to calculate the GCF of 3 and 20 The GCF of 3 and 20 is 1. The ribbon is 1 meter long.</p>

51 <h3>Explanation</h3>

50 <h3>Explanation</h3>

52 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 3 and 20 which is 1. The length of each piece of the ribbon will be 1 meter.</p>

51 <p>For calculating the longest length of the ribbon first we need to calculate the GCF of 3 and 20 which is 1. The length of each piece of the ribbon will be 1 meter.</p>

53 <p>Well explained 👍</p>

52 <p>Well explained 👍</p>

54 <h3>Problem 4</h3>

53 <h3>Problem 4</h3>

55 <p>A carpenter has two wooden planks, one 3 cm long and the other 20 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>

54 <p>A carpenter has two wooden planks, one 3 cm long and the other 20 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>

56 <p>Okay, lets begin</p>

55 <p>Okay, lets begin</p>

57 <p>The carpenter needs the longest piece of wood GCF of 3 and 20 is 1. The longest length of each piece is 1 cm.</p>

56 <p>The carpenter needs the longest piece of wood GCF of 3 and 20 is 1. The longest length of each piece is 1 cm.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>To find the longest length of each piece of the two wooden planks, 3 cm and 20 cm, respectively. We have to find the GCF of 3 and 20, which is 1 cm. The longest length of each piece is 1 cm.</p>

58 <p>To find the longest length of each piece of the two wooden planks, 3 cm and 20 cm, respectively. We have to find the GCF of 3 and 20, which is 1 cm. The longest length of each piece is 1 cm.</p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 5</h3>

60 <h3>Problem 5</h3>

62 <p>If the GCF of 3 and ‘a’ is 1, and the LCM is 60. Find ‘a’.</p>

61 <p>If the GCF of 3 and ‘a’ is 1, and the LCM is 60. Find ‘a’.</p>

63 <p>Okay, lets begin</p>

62 <p>Okay, lets begin</p>

64 <p>The value of ‘a’ is 20.</p>

63 <p>The value of ‘a’ is 20.</p>

65 <h3>Explanation</h3>

64 <h3>Explanation</h3>

66 <p>GCF x LCM = product of the numbers</p>

65 <p>GCF x LCM = product of the numbers</p>

67 <p>1 × 60 = 3 × a</p>

66 <p>1 × 60 = 3 × a</p>

68 <p>60 = 3a</p>

67 <p>60 = 3a</p>

69 <p>a = 60 ÷ 3 = 20</p>

68 <p>a = 60 ÷ 3 = 20</p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQs on the Greatest Common Factor of 3 and 20</h2>

70 <h2>FAQs on the Greatest Common Factor of 3 and 20</h2>

72 <h3>1.What is the LCM of 3 and 20?</h3>

71 <h3>1.What is the LCM of 3 and 20?</h3>

73 <p>The LCM of 3 and 20 is 60.</p>

72 <p>The LCM of 3 and 20 is 60.</p>

74 <h3>2.Is 3 divisible by 2?</h3>

73 <h3>2.Is 3 divisible by 2?</h3>

75 <p>No, 3 is not divisible by 2 because it is an<a>odd number</a>.</p>

74 <p>No, 3 is not divisible by 2 because it is an<a>odd number</a>.</p>

76 <h3>3.What will be the GCF of any two prime numbers?</h3>

75 <h3>3.What will be the GCF of any two prime numbers?</h3>

77 <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>

76 <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>

78 <h3>4.What is the prime factorization of 20?</h3>

77 <h3>4.What is the prime factorization of 20?</h3>

79 <p>The prime factorization of 20 is 2² x 5.</p>

78 <p>The prime factorization of 20 is 2² x 5.</p>

80 <h3>5.Are 3 and 20 prime numbers?</h3>

79 <h3>5.Are 3 and 20 prime numbers?</h3>

81 <p>3 is a prime number, but 20 is not because it has more than two factors.</p>

80 <p>3 is a prime number, but 20 is not because it has more than two factors.</p>

82 <h2>Important Glossaries for GCF of 3 and 20</h2>

81 <h2>Important Glossaries for GCF of 3 and 20</h2>

83 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

82 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.</li>

84 </ul><ul><li><strong>Prime Numbers:</strong>Numbers that have only two factors, 1 and the number itself. For example, 3 is a prime number.</li>

83 </ul><ul><li><strong>Prime Numbers:</strong>Numbers that have only two factors, 1 and the number itself. For example, 3 is a prime number.</li>

85 </ul><ul><li><strong>Common Factor:</strong>A number that is a factor of two or more numbers. The common factor of 3 and 20 is 1.</li>

84 </ul><ul><li><strong>Common Factor:</strong>A number that is a factor of two or more numbers. The common factor of 3 and 20 is 1.</li>

86 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 3 and 20 is 1.</li>

85 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 3 and 20 is 1.</li>

87 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers. For example, the LCM of 3 and 20 is 60.</li>

86 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers. For example, the LCM of 3 and 20 is 60.</li>

88 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

87 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

89 <p>▶</p>

88 <p>▶</p>

90 <h2>Hiralee Lalitkumar Makwana</h2>

89 <h2>Hiralee Lalitkumar Makwana</h2>

91 <h3>About the Author</h3>

90 <h3>About the Author</h3>

92 <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>

91 <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>

93 <h3>Fun Fact</h3>

92 <h3>Fun Fact</h3>

94 <p>: She loves to read number jokes and games.</p>

93 <p>: She loves to read number jokes and games.</p>