What is the Greatest Common Factor of 31872 and 31888?

Greatest common factor (GCF) of 31872 and 31888 is 16.

GCF(31872,31888) = 16

We will now calculate the prime factors of 31872 and 31888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31872 and 31888.

How to find the GCF of 31872 and 31888?

We will first find the prime factorization of 31872 and 31888. After we will calculate the factors of 31872 and 31888 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 31888

Prime factors of 31888 are 2, 1993. Prime factorization of 31888 in exponential form is:

31888 = 2⁴ × 1993¹

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 31888

List of positive integer factors of 31888 that divides 31872 without a remainder.

1, 2, 4, 8, 16, 1993, 3986, 7972, 15944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31872 and 31888. The biggest common factor number is the GCF number.
So the greatest common factor 31872 and 31888 is 16.

Also check out the Least Common Multiple of 31872 and 31888