What is the Greatest Common Factor of 65 and 78?

Greatest common factor (GCF) of 65 and 78 is 13.

GCF(65,78) = 13

We will now calculate the prime factors of 65 and 78, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65 and 78.

How to find the GCF of 65 and 78?

We will first find the prime factorization of 65 and 78. After we will calculate the factors of 65 and 78 and find the biggest common factor number .

Step-1: Prime Factorization of 65

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

65 = 5¹ × 13¹

Step-2: Prime Factorization of 78

Prime factors of 78 are 2, 3, 13. Prime factorization of 78 in exponential form is:

78 = 2¹ × 3¹ × 13¹

Step-3: Factors of 65

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

1, 5, 13

Step-4: Factors of 78

List of positive integer factors of 78 that divides 65 without a remainder.

1, 2, 3, 6, 13, 26, 39

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65 and 78. The biggest common factor number is the GCF number.
So the greatest common factor 65 and 78 is 13.

Also check out the Least Common Multiple of 65 and 78