What is the Greatest Common Factor of 31872 and 31884?

Greatest common factor (GCF) of 31872 and 31884 is 12.

GCF(31872,31884) = 12

We will now calculate the prime factors of 31872 and 31884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31872 and 31884.

How to find the GCF of 31872 and 31884?

We will first find the prime factorization of 31872 and 31884. After we will calculate the factors of 31872 and 31884 and find the biggest common factor number .

Step-1: Prime Factorization of 31872

Prime factors of 31872 are 2, 3, 83. Prime factorization of 31872 in exponential form is:

31872 = 2⁷ × 3¹ × 83¹

Step-2: Prime Factorization of 31884

Prime factors of 31884 are 2, 3, 2657. Prime factorization of 31884 in exponential form is:

31884 = 2² × 3¹ × 2657¹

Step-3: Factors of 31872

List of positive integer factors of 31872 that divides 31872 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 83, 96, 128, 166, 192, 249, 332, 384, 498, 664, 996, 1328, 1992, 2656, 3984, 5312, 7968, 10624, 15936

Step-4: Factors of 31884

List of positive integer factors of 31884 that divides 31872 without a remainder.

1, 2, 3, 4, 6, 12, 2657, 5314, 7971, 10628, 15942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31872 and 31884. The biggest common factor number is the GCF number.
So the greatest common factor 31872 and 31884 is 12.

Also check out the Least Common Multiple of 31872 and 31884