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102 LearnersLast updated on September 10, 2025
GCF of 17 and 51
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 17 and 51.
What is the GCF of 17 and 51?
The greatest common factor of 17 and 51 is 17. The largest divisor of two or more numbers 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. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 17 and 51?
To find the GCF of 17 and 51, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 17 and 51 by Using Listing of factors
Steps to find the GCF of 17 and 51 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 17 = 1, 17.
Factors of 51 = 1, 3, 17, 51.
Step 2: Now, identify the common factors of them Common factors of 17 and 51: 1, 17.
Step 3: Choose the largest factor The largest factor that both numbers have is 17. The GCF of 17 and 51 is 17.
GCF of 17 and 51 Using Prime Factorization
To find the GCF of 17 and 51 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 17: 17 = 17
Prime Factors of 51: 51 = 3 x 17
Step 2: Now, identify the common prime factors The common prime factor is 17
Step 3: Multiply the common prime factors The Greatest Common Factor of 17 and 51 is 17.
GCF of 17 and 51 Using Division Method or Euclidean Algorithm Method
Find the GCF of 17 and 51 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 51 by 17 51 ÷ 17 = 3 (quotient), remainder = 51 - (17x3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 17 and 51 is 17.
Common Mistakes and How to Avoid Them in GCF of 17 and 51
Finding the GCF of 17 and 51 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 51, students may mention 5, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 17 and 51 Examples
Problem 1
A farmer has 17 apple trees and 51 orange trees. He wants to plant them in rows with the same number of trees in each row. How many trees will be in each row?
We should find the GCF of 17 and 51 GCF of 17 and 51 is 17.
There are 17 equal groups 17 ÷ 17 = 1
51 ÷ 17 = 3
There will be 17 trees in each row.
Explanation
As the GCF of 17 and 51 is 17, the farmer can make rows with 17 trees each. Now divide 17 and 51 by 17 to find how many trees are in each row.
Problem 2
A chef has 17 kilograms of flour and 51 kilograms of sugar. He wants to package them into smaller bags with the same weight. What should be the weight of each bag?
GCF of 17 and 51 is 17. So each bag will contain 17 kilograms.
Explanation
There are 17 kilograms of flour and 51 kilograms of sugar. To find the weight of each bag, we should find the GCF of 17 and 51. Each bag will contain 17 kilograms.
Problem 3
A teacher has 17 notebooks and 51 pens. She wants to distribute them equally among her students. How many students can she distribute them to?
For equal distribution, we have to calculate the GCF of 17 and 51 The GCF of 17 and 51 is 17. She can distribute them to 17 students.
Explanation
For equal distribution, we need to calculate the GCF of 17 and 51, which is 17. The number of students will be 17.
Problem 4
A construction worker has two ropes, one 17 meters long and the other 51 meters long. He wants to cut them into the longest possible equal pieces, without any rope left over. What should be the length of each piece?
The worker needs the longest piece of rope GCF of 17 and 51 is 17. The longest length of each piece is 17 meters.
Explanation
To find the longest length of each piece of the two ropes, 17 meters and 51 meters respectively, we have to find the GCF of 17 and 51, which is 17 meters. The longest length of each piece is 17 meters.
Problem 5
If the GCF of 17 and ‘b’ is 17, and the LCM is 51, find ‘b’.
The value of ‘b’ is 51.
Explanation
GCF x LCM = product of the numbers
17 × 51 = 17 × b
867 = 17b
b = 867 ÷ 17 = 51
FAQs on the Greatest Common Factor of 17 and 51
1.What is the LCM of 17 and 51?
2.Is 17 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 51?
5.Are 17 and 51 co-prime numbers?
6.How can families in United States create number-rich environments to improve GCF of 17 and 51 skills?
7.What are some fun ways kids in United States can practice GCF of 17 and 51 with numbers?
8.What role do numbers and GCF of 17 and 51 play in helping children in United States develop problem-solving skills?
9.How can children in United States use numbers in everyday life to understand GCF of 17 and 51?
Important Glossaries for GCF of 17 and 51
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 17 are 1 and 17.
- Prime Number: A number that has only two factors, 1 and itself. For example, 17 is a prime number.
- Prime Factors: 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.
- Common Factors: Numbers that are factors of two or more numbers. For example, the common factors of 17 and 51 are 1 and 17.
- Euclidean Algorithm: A method for finding the greatest common divisor of two numbers by using the remainder operation.
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
