What is the Greatest Common Factor of 32102 and 32116?

Greatest common factor (GCF) of 32102 and 32116 is 14.

GCF(32102,32116) = 14

We will now calculate the prime factors of 32102 and 32116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32102 and 32116.

How to find the GCF of 32102 and 32116?

We will first find the prime factorization of 32102 and 32116. After we will calculate the factors of 32102 and 32116 and find the biggest common factor number .

Step-1: Prime Factorization of 32102

Prime factors of 32102 are 2, 7, 2293. Prime factorization of 32102 in exponential form is:

32102 = 2¹ × 7¹ × 2293¹

Step-2: Prime Factorization of 32116

Prime factors of 32116 are 2, 7, 31, 37. Prime factorization of 32116 in exponential form is:

32116 = 2² × 7¹ × 31¹ × 37¹

Step-3: Factors of 32102

List of positive integer factors of 32102 that divides 32102 without a remainder.

1, 2, 7, 14, 2293, 4586, 16051

Step-4: Factors of 32116

List of positive integer factors of 32116 that divides 32102 without a remainder.

1, 2, 4, 7, 14, 28, 31, 37, 62, 74, 124, 148, 217, 259, 434, 518, 868, 1036, 1147, 2294, 4588, 8029, 16058

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32102 and 32116. The biggest common factor number is the GCF number.
So the greatest common factor 32102 and 32116 is 14.

Also check out the Least Common Multiple of 32102 and 32116