What is the Greatest Common Factor of 51 and 65?

Greatest common factor (GCF) of 51 and 65 is 1.

GCF(51,65) = 1

We will now calculate the prime factors of 51 and 65, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51 and 65.

How to find the GCF of 51 and 65?

We will first find the prime factorization of 51 and 65. After we will calculate the factors of 51 and 65 and find the biggest common factor number .

Step-1: Prime Factorization of 51

Prime factors of 51 are 3, 17. Prime factorization of 51 in exponential form is:

51 = 3¹ × 17¹

Step-2: Prime Factorization of 65

Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:

65 = 5¹ × 13¹

Step-3: Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1, 3, 17

Step-4: Factors of 65

List of positive integer factors of 65 that divides 51 without a remainder.

1, 5, 13

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 51 and 65 is 1.

Also check out the Least Common Multiple of 51 and 65