What is the Greatest Common Factor of 31664 and 31684?

Greatest common factor (GCF) of 31664 and 31684 is 4.

GCF(31664,31684) = 4

We will now calculate the prime factors of 31664 and 31684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31664 and 31684.

How to find the GCF of 31664 and 31684?

We will first find the prime factorization of 31664 and 31684. After we will calculate the factors of 31664 and 31684 and find the biggest common factor number .

Step-1: Prime Factorization of 31664

Prime factors of 31664 are 2, 1979. Prime factorization of 31664 in exponential form is:

31664 = 2⁴ × 1979¹

Step-2: Prime Factorization of 31684

Prime factors of 31684 are 2, 89. Prime factorization of 31684 in exponential form is:

31684 = 2² × 89²

Step-3: Factors of 31664

List of positive integer factors of 31664 that divides 31664 without a remainder.

1, 2, 4, 8, 16, 1979, 3958, 7916, 15832

Step-4: Factors of 31684

List of positive integer factors of 31684 that divides 31664 without a remainder.

1, 2, 4, 89, 178, 356, 7921, 15842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31664 and 31684. The biggest common factor number is the GCF number.
So the greatest common factor 31664 and 31684 is 4.

Also check out the Least Common Multiple of 31664 and 31684