What is the Greatest Common Factor of 65975 and 65982?

Greatest common factor (GCF) of 65975 and 65982 is 7.

GCF(65975,65982) = 7

We will now calculate the prime factors of 65975 and 65982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65975 and 65982.

How to find the GCF of 65975 and 65982?

We will first find the prime factorization of 65975 and 65982. After we will calculate the factors of 65975 and 65982 and find the biggest common factor number .

Step-1: Prime Factorization of 65975

Prime factors of 65975 are 5, 7, 13, 29. Prime factorization of 65975 in exponential form is:

65975 = 5² × 7¹ × 13¹ × 29¹

Step-2: Prime Factorization of 65982

Prime factors of 65982 are 2, 3, 7, 1571. Prime factorization of 65982 in exponential form is:

65982 = 2¹ × 3¹ × 7¹ × 1571¹

Step-3: Factors of 65975

List of positive integer factors of 65975 that divides 65975 without a remainder.

1, 5, 7, 13, 25, 29, 35, 65, 91, 145, 175, 203, 325, 377, 455, 725, 1015, 1885, 2275, 2639, 5075, 9425, 13195

Step-4: Factors of 65982

List of positive integer factors of 65982 that divides 65975 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1571, 3142, 4713, 9426, 10997, 21994, 32991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65975 and 65982. The biggest common factor number is the GCF number.
So the greatest common factor 65975 and 65982 is 7.

Also check out the Least Common Multiple of 65975 and 65982