What is the Greatest Common Factor of 31129 and 31136?

Greatest common factor (GCF) of 31129 and 31136 is 7.

GCF(31129,31136) = 7

We will now calculate the prime factors of 31129 and 31136, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31129 and 31136.

How to find the GCF of 31129 and 31136?

We will first find the prime factorization of 31129 and 31136. After we will calculate the factors of 31129 and 31136 and find the biggest common factor number .

Step-1: Prime Factorization of 31129

Prime factors of 31129 are 7, 4447. Prime factorization of 31129 in exponential form is:

31129 = 7¹ × 4447¹

Step-2: Prime Factorization of 31136

Prime factors of 31136 are 2, 7, 139. Prime factorization of 31136 in exponential form is:

31136 = 2⁵ × 7¹ × 139¹

Step-3: Factors of 31129

List of positive integer factors of 31129 that divides 31129 without a remainder.

1, 7, 4447

Step-4: Factors of 31136

List of positive integer factors of 31136 that divides 31129 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 139, 224, 278, 556, 973, 1112, 1946, 2224, 3892, 4448, 7784, 15568

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31129 and 31136. The biggest common factor number is the GCF number.
So the greatest common factor 31129 and 31136 is 7.

Also check out the Least Common Multiple of 31129 and 31136