What is the Greatest Common Factor of 65314 and 65331?

Greatest common factor (GCF) of 65314 and 65331 is 17.

GCF(65314,65331) = 17

We will now calculate the prime factors of 65314 and 65331, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65314 and 65331.

How to find the GCF of 65314 and 65331?

We will first find the prime factorization of 65314 and 65331. After we will calculate the factors of 65314 and 65331 and find the biggest common factor number .

Step-1: Prime Factorization of 65314

Prime factors of 65314 are 2, 17, 113. Prime factorization of 65314 in exponential form is:

65314 = 2¹ × 17² × 113¹

Step-2: Prime Factorization of 65331

Prime factors of 65331 are 3, 7, 17, 61. Prime factorization of 65331 in exponential form is:

65331 = 3² × 7¹ × 17¹ × 61¹

Step-3: Factors of 65314

List of positive integer factors of 65314 that divides 65314 without a remainder.

1, 2, 17, 34, 113, 226, 289, 578, 1921, 3842, 32657

Step-4: Factors of 65331

List of positive integer factors of 65331 that divides 65314 without a remainder.

1, 3, 7, 9, 17, 21, 51, 61, 63, 119, 153, 183, 357, 427, 549, 1037, 1071, 1281, 3111, 3843, 7259, 9333, 21777

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65314 and 65331. The biggest common factor number is the GCF number.
So the greatest common factor 65314 and 65331 is 17.

Also check out the Least Common Multiple of 65314 and 65331