Rivalry2

HTML Diff

1 added 2 removed

Original 2026-01-01

Modified 2026-02-28

1 - <p>146 Learners</p>

1 + <p>172 Learners</p>

2 <p>Last updated on<strong>August 6, 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 34 and 51.</p>

4 <h2>What is the GCF of 34 and 51?</h2>

5 <p>The<a>greatest common factor</a><a>of</a>34 and 51 is 17. The largest<a>divisor</a>of two or more<a>numbers</a>is called the GCF of the numbers. 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>

6 <h2>How to find the GCF of 34 and 51?</h2>

7 <p>To find the GCF of 34 and 51, a few methods are described below:</p>

8 <ul><li>Listing Factors</li>

9 </ul><ul><li>Prime Factorization</li>

10 </ul><ul><li>Long Division Method / by Euclidean Algorithm</li>

11 </ul><h3>GCF of 34 and 51 by Using Listing of Factors</h3>

12 <p>Steps to find the GCF of 34 and 51 using the listing of<a>factors</a>:</p>

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

14 <p>Factors of 34 = 1, 2, 17, 34.</p>

15 <p>Factors of 51 = 1, 3, 17, 51.</p>

16 <p><strong>Step 2:</strong>Now, identify the<a>common factors</a>of them.</p>

17 <p>Common factors of 34 and 51: 1, 17.</p>

18 <p><strong>Step 3:</strong>Choose the largest factor:</p>

19 <p>The largest factor that both numbers have is 17.</p>

20 <p>The GCF of 34 and 51 is 17.</p>

21 <h3>Explore Our Programs</h3>

22 - <p>No Courses Available</p>

23 <h3>GCF of 34 and 51 Using Prime Factorization</h3>

22 <h3>GCF of 34 and 51 Using Prime Factorization</h3>

24 <p>To find the GCF of 34 and 51 using the Prime Factorization Method, follow these steps:</p>

23 <p>To find the GCF of 34 and 51 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 34: 34 = 2 x 17</p>

25 <p>Prime Factors of 34: 34 = 2 x 17</p>

27 <p>Prime Factors of 51: 51 = 3 x 17</p>

26 <p>Prime Factors of 51: 51 = 3 x 17</p>

28 <p><strong>Step 2:</strong>Now, identify the common prime factors:</p>

27 <p><strong>Step 2:</strong>Now, identify the common prime factors:</p>

29 <p>The common prime factor is: 17</p>

28 <p>The common prime factor is: 17</p>

30 <p><strong>Step 3:</strong>Multiply the common prime factors.</p>

29 <p><strong>Step 3:</strong>Multiply the common prime factors.</p>

31 <p>The Greatest Common Factor of 34 and 51 is 17.</p>

30 <p>The Greatest Common Factor of 34 and 51 is 17.</p>

32 <h3>GCF of 34 and 51 Using Division Method or Euclidean Algorithm Method</h3>

31 <h3>GCF of 34 and 51 Using Division Method or Euclidean Algorithm Method</h3>

33 <p>Find the GCF of 34 and 51 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

32 <p>Find the GCF of 34 and 51 using the<a>division</a>method or Euclidean Algorithm Method. Follow these steps:</p>

34 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number.</p>

33 <p><strong>Step 1:</strong>First, divide the larger number by the smaller number.</p>

35 <p>Here, divide 51 by 34 51 ÷ 34 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 51 - (34x1) = 17</p>

34 <p>Here, divide 51 by 34 51 ÷ 34 = 1 (<a>quotient</a>), The<a>remainder</a>is calculated as 51 - (34x1) = 17</p>

36 <p>The remainder is 17, not zero, so continue the process</p>

35 <p>The remainder is 17, not zero, so continue the process</p>

37 <p><strong>Step 2:</strong>Now divide the previous divisor (34) by the previous remainder (17)</p>

36 <p><strong>Step 2:</strong>Now divide the previous divisor (34) by the previous remainder (17)</p>

38 <p>Divide 34 by 17 34 ÷ 17 = 2 (quotient), remainder = 34 - (17x2) = 0</p>

37 <p>Divide 34 by 17 34 ÷ 17 = 2 (quotient), remainder = 34 - (17x2) = 0</p>

39 <p>The remainder is zero, the divisor will become the GCF.</p>

38 <p>The remainder is zero, the divisor will become the GCF.</p>

40 <p>The GCF of 34 and 51 is 17.</p>

39 <p>The GCF of 34 and 51 is 17.</p>

41 <h2>Common Mistakes and How to Avoid Them in GCF of 34 and 51</h2>

40 <h2>Common Mistakes and How to Avoid Them in GCF of 34 and 51</h2>

42 <p>Finding GCF of 34 and 51 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

41 <p>Finding GCF of 34 and 51 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.</p>

43 <h3>Problem 1</h3>

42 <h3>Problem 1</h3>

44 <p>A gardener has 34 tulips and 51 daisies. She wants to plant them in equal rows with the largest number of flowers in each row. How many flowers will be in each row?</p>

43 <p>A gardener has 34 tulips and 51 daisies. She wants to plant them in equal rows with the largest number of flowers in each row. How many flowers will be in each row?</p>

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

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

46 <p>We should find the GCF of 34 and 51.</p>

45 <p>We should find the GCF of 34 and 51.</p>

47 <p>GCF of 34 and 51 is 17.</p>

46 <p>GCF of 34 and 51 is 17.</p>

48 <p>There are 17 equal groups.</p>

47 <p>There are 17 equal groups.</p>

49 <p>34 ÷ 17 = 2</p>

48 <p>34 ÷ 17 = 2</p>

50 <p>51 ÷ 17 = 3</p>

49 <p>51 ÷ 17 = 3</p>

51 <p>There will be 17 groups, and each row gets 2 tulips and 3 daisies.</p>

50 <p>There will be 17 groups, and each row gets 2 tulips and 3 daisies.</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>As the GCF of 34 and 51 is 17, the gardener can make 17 groups.</p>

52 <p>As the GCF of 34 and 51 is 17, the gardener can make 17 groups.</p>

54 <p>Now divide 34 and 51 by 17.</p>

53 <p>Now divide 34 and 51 by 17.</p>

55 <p>Each row gets 2 tulips and 3 daisies.</p>

54 <p>Each row gets 2 tulips and 3 daisies.</p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 2</h3>

56 <h3>Problem 2</h3>

58 <p>A bakery has 34 croissants and 51 muffins. They want to package them in boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?</p>

57 <p>A bakery has 34 croissants and 51 muffins. They want to package them in boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?</p>

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

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

60 <p>GCF of 34 and 51 is 17.</p>

59 <p>GCF of 34 and 51 is 17.</p>

61 <p>So each box will have 17 items.</p>

60 <p>So each box will have 17 items.</p>

62 <h3>Explanation</h3>

61 <h3>Explanation</h3>

63 <p>There are 34 croissants and 51 muffins.</p>

62 <p>There are 34 croissants and 51 muffins.</p>

64 <p>To find the total number of items in each box, we should find the GCF of 34 and 51.</p>

63 <p>To find the total number of items in each box, we should find the GCF of 34 and 51.</p>

65 <p>There will be 17 items in each box.</p>

64 <p>There will be 17 items in each box.</p>

66 <p>Well explained 👍</p>

65 <p>Well explained 👍</p>

67 <h3>Problem 3</h3>

66 <h3>Problem 3</h3>

68 <p>A tailor has 34 meters of silk and 51 meters of cotton 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>

67 <p>A tailor has 34 meters of silk and 51 meters of cotton 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>

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

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

70 <p>For calculating the longest equal length, we have to calculate the GCF of 34 and 51.</p>

69 <p>For calculating the longest equal length, we have to calculate the GCF of 34 and 51.</p>

71 <p>The GCF of 34 and 51 is 17.</p>

70 <p>The GCF of 34 and 51 is 17.</p>

72 <p>The fabric is 17 meters long.</p>

71 <p>The fabric is 17 meters long.</p>

73 <h3>Explanation</h3>

72 <h3>Explanation</h3>

74 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 34 and 51, which is 17.</p>

73 <p>For calculating the longest length of the fabric, first we need to calculate the GCF of 34 and 51, which is 17.</p>

75 <p>The length of each piece of fabric will be 17 meters.</p>

74 <p>The length of each piece of fabric will be 17 meters.</p>

76 <p>Well explained 👍</p>

75 <p>Well explained 👍</p>

77 <h3>Problem 4</h3>

76 <h3>Problem 4</h3>

78 <p>A carpenter has two wooden planks, one 34 cm long and the other 51 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>

77 <p>A carpenter has two wooden planks, one 34 cm long and the other 51 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>

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

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

80 <p>The carpenter needs the longest piece of wood.</p>

79 <p>The carpenter needs the longest piece of wood.</p>

81 <p>GCF of 34 and 51 is 17.</p>

80 <p>GCF of 34 and 51 is 17.</p>

82 <p>The longest length of each piece is 17 cm.</p>

81 <p>The longest length of each piece is 17 cm.</p>

83 <h3>Explanation</h3>

82 <h3>Explanation</h3>

84 <p>To find the longest length of each piece of the two wooden planks, 34 cm and 51 cm, respectively, we have to find the GCF of 34 and 51, which is 17 cm. The longest length of each piece is 17 cm.</p>

83 <p>To find the longest length of each piece of the two wooden planks, 34 cm and 51 cm, respectively, we have to find the GCF of 34 and 51, which is 17 cm. The longest length of each piece is 17 cm.</p>

85 <p>Well explained 👍</p>

84 <p>Well explained 👍</p>

86 <h3>Problem 5</h3>

85 <h3>Problem 5</h3>

87 <p>If the GCF of 34 and ‘b’ is 17, and the LCM is 102. Find ‘b’.</p>

86 <p>If the GCF of 34 and ‘b’ is 17, and the LCM is 102. Find ‘b’.</p>

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

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

89 <p>The value of ‘b’ is 51.</p>

88 <p>The value of ‘b’ is 51.</p>

90 <h3>Explanation</h3>

89 <h3>Explanation</h3>

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

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

92 <p>17 x 102 = 34 x b</p>

91 <p>17 x 102 = 34 x b</p>

93 <p>1734 = 34b</p>

92 <p>1734 = 34b</p>

94 <p>b = 1734 ÷ 34 = 51</p>

93 <p>b = 1734 ÷ 34 = 51</p>

95 <p>Well explained 👍</p>

94 <p>Well explained 👍</p>

96 <h2>FAQs on the Greatest Common Factor of 34 and 51</h2>

95 <h2>FAQs on the Greatest Common Factor of 34 and 51</h2>

97 <h3>1.What is the LCM of 34 and 51?</h3>

96 <h3>1.What is the LCM of 34 and 51?</h3>

98 <p>The LCM of 34 and 51 is 102.</p>

97 <p>The LCM of 34 and 51 is 102.</p>

99 <h3>2.Is 34 divisible by 2?</h3>

98 <h3>2.Is 34 divisible by 2?</h3>

100 <p>Yes, 34 is divisible by 2 because it is an even number.</p>

99 <p>Yes, 34 is divisible by 2 because it is an even number.</p>

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

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

102 <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>

101 <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>

103 <h3>4.What is the prime factorization of 51?</h3>

102 <h3>4.What is the prime factorization of 51?</h3>

104 <p>The prime factorization of 51 is 3 x 17.</p>

103 <p>The prime factorization of 51 is 3 x 17.</p>

105 <h3>5.Are 34 and 51 prime numbers?</h3>

104 <h3>5.Are 34 and 51 prime numbers?</h3>

106 <p>No, 34 and 51 are not prime numbers because both of them have more than two factors.</p>

105 <p>No, 34 and 51 are not prime numbers because both of them have more than two factors.</p>

107 <h2>Important Glossaries for GCF of 34 and 51</h2>

106 <h2>Important Glossaries for GCF of 34 and 51</h2>

108 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 17 are 1 and 17.</li>

107 <ul><li><strong>Factors:</strong>Factors are numbers that divide the target number completely. For example, the factors of 17 are 1 and 17.</li>

109 </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 51 are 3 and 17.</li>

108 </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 51 are 3 and 17.</li>

110 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 51 is divided by 34, the remainder is 17.</li>

109 </ul><ul><li><strong>Remainder:</strong>The value left after division when the number cannot be divided evenly. For example, when 51 is divided by 34, the remainder is 17.</li>

111 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 34 and 51 is 102.</li>

110 </ul><ul><li><strong>LCM:</strong>The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 34 and 51 is 102.</li>

112 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 34 and 51 is 17, as it is their largest common factor that divides the numbers completely.</li>

111 </ul><ul><li><strong>GCF:</strong>The largest factor that commonly divides two or more numbers. For example, the GCF of 34 and 51 is 17, as it is their largest common factor that divides the numbers completely.</li>

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

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

114 <p>▶</p>

113 <p>▶</p>

115 <h2>Hiralee Lalitkumar Makwana</h2>

114 <h2>Hiralee Lalitkumar Makwana</h2>

116 <h3>About the Author</h3>

115 <h3>About the Author</h3>

117 <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>

116 <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>

118 <h3>Fun Fact</h3>

117 <h3>Fun Fact</h3>

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

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