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1 - <p>119 Learners</p>

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2 <p>Last updated on<strong>September 24, 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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 4, 6, and 3.</p>

4 <h2>What is the GCF of 4, 6, and 3?</h2>

5 <p>The<a>greatest common factor</a>of 4, 6, and 3 is 1. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. If numbers are co-prime, they have no common factors other than 1, so their GCF is 1.</p>

6 <p>The GCF of numbers cannot be negative because divisors are always positive.</p>

7 <h2>How to find the GCF of 4, 6, and 3?</h2>

8 <p>To find the GCF of 4, 6, and 3, a few methods are described below </p>

9 <ul><li>Listing Factors </li>

10 <li>Prime Factorization </li>

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

12 </ul><h2>GCF of 4, 6, and 3 by Using Listing of Factors</h2>

13 <p>Steps to find the GCF of 4, 6, and 3 using the listing of<a>factors</a></p>

14 <p><strong>Step 1:</strong>Firstly, list the factors of each number</p>

15 <p>Factors of 4 = 1, 2, 4.</p>

16 <p>Factors of 6 = 1, 2, 3, 6.</p>

17 <p>Factors of 3 = 1, 3.</p>

18 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them Common factor of 4, 6, and 3: 1.</p>

19 <p><strong>Step 3:</strong>Choose the largest factor The largest factor that all the numbers have is 1.</p>

20 <p>The GCF of 4, 6, and 3 is 1.</p>

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23 <h2>GCF of 4, 6, and 3 Using Prime Factorization</h2>

22 <h2>GCF of 4, 6, and 3 Using Prime Factorization</h2>

24 <p>To find the GCF of 4, 6, and 3 using the Prime Factorization Method, follow these steps:</p>

23 <p>To find the GCF of 4, 6, and 3 using the Prime Factorization Method, follow these steps:</p>

25 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

24 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of each number</p>

26 <p>Prime Factors of 4: 4 = 2 x 2 = 2²</p>

25 <p>Prime Factors of 4: 4 = 2 x 2 = 2²</p>

27 <p>Prime Factors of 6: 6 = 2 x 3</p>

26 <p>Prime Factors of 6: 6 = 2 x 3</p>

28 <p>Prime Factors of 3: 3 = 3</p>

27 <p>Prime Factors of 3: 3 = 3</p>

29 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: None, as there is no common prime factor other than 1.</p>

28 <p><strong>Step 2:</strong>Now, identify the common prime factors The common prime factor is: None, as there is no common prime factor other than 1.</p>

30 <p><strong>Step 3:</strong>Since there's no common prime factor other than 1, the GCF is 1.</p>

29 <p><strong>Step 3:</strong>Since there's no common prime factor other than 1, the GCF is 1.</p>

31 <p>The Greatest Common Factor of 4, 6, and 3 is 1.</p>

30 <p>The Greatest Common Factor of 4, 6, and 3 is 1.</p>

32 <h2>GCF of 4, 6, and 3 Using Division Method or Euclidean Algorithm Method</h2>

31 <h2>GCF of 4, 6, and 3 Using Division Method or Euclidean Algorithm Method</h2>

33 <p>Find the GCF of 4, 6, and 3 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

32 <p>Find the GCF of 4, 6, and 3 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

34 <p><strong>Step 1:</strong>First, choose any two numbers, such as 4 and 6.</p>

33 <p><strong>Step 1:</strong>First, choose any two numbers, such as 4 and 6.</p>

35 <p>Divide the larger number by the smaller number 6 ÷ 4 = 1 (<a>quotient</a>),<a>remainder</a>= 6 - (4×1) = 2</p>

34 <p>Divide the larger number by the smaller number 6 ÷ 4 = 1 (<a>quotient</a>),<a>remainder</a>= 6 - (4×1) = 2</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (4) by the previous remainder (2) 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0</p>

35 <p><strong>Step 2:</strong>Now divide the previous divisor (4) by the previous remainder (2) 4 ÷ 2 = 2 (quotient), remainder = 4 - (2×2) = 0</p>

37 <p>The remainder is zero, so the GCF of 4 and 6 is 2.</p>

36 <p>The remainder is zero, so the GCF of 4 and 6 is 2.</p>

38 <p><strong>Step 3:</strong>Compare the GCF of 4 and 6 with the next number (3).</p>

37 <p><strong>Step 3:</strong>Compare the GCF of 4 and 6 with the next number (3).</p>

39 <p>Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 - (2×1) = 1</p>

38 <p>Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 - (2×1) = 1</p>

40 <p><strong>Step 4:</strong>Divide the previous divisor (2) by the remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 - (1×2) = 0</p>

39 <p><strong>Step 4:</strong>Divide the previous divisor (2) by the remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 - (1×2) = 0</p>

41 <p>The remainder is zero, so the GCF of 4, 6, and 3 is 1.</p>

40 <p>The remainder is zero, so the GCF of 4, 6, and 3 is 1.</p>

42 <h2>Common Mistakes and How to Avoid Them in GCF of 4, 6, and 3</h2>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 4, 6, and 3</h2>

43 <p>Finding the GCF of 4, 6, and 3 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

42 <p>Finding the GCF of 4, 6, and 3 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

44 <h3>Problem 1</h3>

43 <h3>Problem 1</h3>

45 <p>A chef has 4 apples, 6 bananas, and 3 oranges. She wants to create fruit baskets with the same number of each fruit in each basket. How many fruit baskets can she make?</p>

44 <p>A chef has 4 apples, 6 bananas, and 3 oranges. She wants to create fruit baskets with the same number of each fruit in each basket. How many fruit baskets can she make?</p>

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

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

47 <p>We should find the GCF of 4, 6, and 3. GCF of 4, 6, and 3 is 1.</p>

46 <p>We should find the GCF of 4, 6, and 3. GCF of 4, 6, and 3 is 1.</p>

48 <p>There will be 1 basket, and each basket will have 4 apples, 6 bananas, and 3 oranges.</p>

47 <p>There will be 1 basket, and each basket will have 4 apples, 6 bananas, and 3 oranges.</p>

49 <h3>Explanation</h3>

48 <h3>Explanation</h3>

50 <p>As the GCF of 4, 6, and 3 is 1, the chef can make 1 basket.</p>

49 <p>As the GCF of 4, 6, and 3 is 1, the chef can make 1 basket.</p>

51 <p>Each basket will contain all the fruits she has.</p>

50 <p>Each basket will contain all the fruits she has.</p>

52 <p>Well explained 👍</p>

51 <p>Well explained 👍</p>

53 <h3>Problem 2</h3>

52 <h3>Problem 2</h3>

54 <p>A gardener has 4 rose bushes, 6 tulip plants, and 3 daffodil plants. She wants to plant them in rows with the same number of each type of plant per row. How many rows can she create?</p>

53 <p>A gardener has 4 rose bushes, 6 tulip plants, and 3 daffodil plants. She wants to plant them in rows with the same number of each type of plant per row. How many rows can she create?</p>

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

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

56 <p>GCF of 4, 6, and 3 is 1.</p>

55 <p>GCF of 4, 6, and 3 is 1.</p>

57 <p>So she can create 1 row.</p>

56 <p>So she can create 1 row.</p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>To find the total number of rows, we should find the GCF of 4, 6, and 3.</p>

58 <p>To find the total number of rows, we should find the GCF of 4, 6, and 3.</p>

60 <p>There will be 1 row, with each row containing all the plants she has.</p>

59 <p>There will be 1 row, with each row containing all the plants she has.</p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h3>Problem 3</h3>

61 <h3>Problem 3</h3>

63 <p>A jeweler has 4 gold chains, 6 silver necklaces, and 3 platinum rings. He wants to display them in equal-sized sets. What should be the number of sets?</p>

62 <p>A jeweler has 4 gold chains, 6 silver necklaces, and 3 platinum rings. He wants to display them in equal-sized sets. What should be the number of sets?</p>

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

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

65 <p>To calculate the number of equal-sized sets, we have to calculate the GCF of 4, 6, and 3.</p>

64 <p>To calculate the number of equal-sized sets, we have to calculate the GCF of 4, 6, and 3.</p>

66 <p>The GCF of 4, 6, and 3 is 1.</p>

65 <p>The GCF of 4, 6, and 3 is 1.</p>

67 <p>There will be 1 set.</p>

66 <p>There will be 1 set.</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>For calculating the number of equal-sized sets, first we need to calculate the GCF of 4, 6, and 3, which is 1.</p>

68 <p>For calculating the number of equal-sized sets, first we need to calculate the GCF of 4, 6, and 3, which is 1.</p>

70 <p>The jeweler will have 1 set, with all the items displayed together.</p>

69 <p>The jeweler will have 1 set, with all the items displayed together.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h3>Problem 4</h3>

71 <h3>Problem 4</h3>

73 <p>A painter has 4 buckets of red paint, 6 buckets of blue paint, and 3 buckets of yellow paint. He wants to distribute them into groups with the same number of each color. How many groups can he make?</p>

72 <p>A painter has 4 buckets of red paint, 6 buckets of blue paint, and 3 buckets of yellow paint. He wants to distribute them into groups with the same number of each color. How many groups can he make?</p>

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

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

75 <p>The painter needs to know the number of groups.</p>

74 <p>The painter needs to know the number of groups.</p>

76 <p>GCF of 4, 6, and 3 is 1.</p>

75 <p>GCF of 4, 6, and 3 is 1.</p>

77 <p>He can make 1 group.</p>

76 <p>He can make 1 group.</p>

78 <h3>Explanation</h3>

77 <h3>Explanation</h3>

79 <p>To find the number of groups he can make, we have to find the GCF of 4, 6, and 3, which is 1.</p>

78 <p>To find the number of groups he can make, we have to find the GCF of 4, 6, and 3, which is 1.</p>

80 <p>He can make 1 group containing all the buckets.</p>

79 <p>He can make 1 group containing all the buckets.</p>

81 <p>Well explained 👍</p>

80 <p>Well explained 👍</p>

82 <h3>Problem 5</h3>

81 <h3>Problem 5</h3>

83 <p>If the GCF of 4 and 'b' is 1, and the LCM is 12, find 'b'.</p>

82 <p>If the GCF of 4 and 'b' is 1, and the LCM is 12, find 'b'.</p>

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

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

85 <p>The value of 'b' is 12.</p>

84 <p>The value of 'b' is 12.</p>

86 <h3>Explanation</h3>

85 <h3>Explanation</h3>

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

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

88 <p>1 × 12 = 4 × b</p>

87 <p>1 × 12 = 4 × b</p>

89 <p>12 = 4b</p>

88 <p>12 = 4b</p>

90 <p>b = 12 ÷ 4 = 3</p>

89 <p>b = 12 ÷ 4 = 3</p>

91 <p>Well explained 👍</p>

90 <p>Well explained 👍</p>

92 <h2>FAQs on the Greatest Common Factor of 4, 6, and 3</h2>

91 <h2>FAQs on the Greatest Common Factor of 4, 6, and 3</h2>

93 <h3>1.What is the LCM of 4, 6, and 3?</h3>

92 <h3>1.What is the LCM of 4, 6, and 3?</h3>

94 <p>The LCM of 4, 6, and 3 is 12.</p>

93 <p>The LCM of 4, 6, and 3 is 12.</p>

95 <h3>2.Is 4 divisible by 2?</h3>

94 <h3>2.Is 4 divisible by 2?</h3>

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

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

97 <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>

96 <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>

98 <h3>4.What is the prime factorization of 6?</h3>

97 <h3>4.What is the prime factorization of 6?</h3>

99 <p>The prime factorization of 6 is 2 × 3.</p>

98 <p>The prime factorization of 6 is 2 × 3.</p>

100 <h3>5.Are 4, 6, and 3 prime numbers?</h3>

99 <h3>5.Are 4, 6, and 3 prime numbers?</h3>

101 <p>No, 4, 6, and 3 are not all prime numbers. Only 3 is a prime number.</p>

100 <p>No, 4, 6, and 3 are not all prime numbers. Only 3 is a prime number.</p>

102 <h2>Important Glossaries for GCF of 4, 6, and 3</h2>

101 <h2>Important Glossaries for GCF of 4, 6, and 3</h2>

103 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.</li>

102 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.</li>

104 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

103 </ul><ul><li><strong>Multiple:</strong>Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.</li>

105 </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 4 are 2.</li>

104 </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 4 are 2.</li>

106 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 5 is divided by 2, the remainder is 1 and the quotient is 2.</li>

105 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 5 is divided by 2, the remainder is 1 and the quotient is 2.</li>

107 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 4, 6, and 3 is 12.</li>

106 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 4, 6, and 3 is 12.</li>

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

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

109 <p>▶</p>

108 <p>▶</p>

110 <h2>Hiralee Lalitkumar Makwana</h2>

109 <h2>Hiralee Lalitkumar Makwana</h2>

111 <h3>About the Author</h3>

110 <h3>About the Author</h3>

112 <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>

111 <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>

113 <h3>Fun Fact</h3>

112 <h3>Fun Fact</h3>

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

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