What is the Greatest Common Factor of 31872 and 31878?

Greatest common factor (GCF) of 31872 and 31878 is 6.

GCF(31872,31878) = 6

We will now calculate the prime factors of 31872 and 31878, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31872 and 31878.

How to find the GCF of 31872 and 31878?

We will first find the prime factorization of 31872 and 31878. After we will calculate the factors of 31872 and 31878 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 31878

Prime factors of 31878 are 2, 3, 7, 11, 23. Prime factorization of 31878 in exponential form is:

31878 = 2¹ × 3² × 7¹ × 11¹ × 23¹

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 31878

List of positive integer factors of 31878 that divides 31872 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 23, 33, 42, 46, 63, 66, 69, 77, 99, 126, 138, 154, 161, 198, 207, 231, 253, 322, 414, 462, 483, 506, 693, 759, 966, 1386, 1449, 1518, 1771, 2277, 2898, 3542, 4554, 5313, 10626, 15939

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31872 and 31878. The biggest common factor number is the GCF number.
So the greatest common factor 31872 and 31878 is 6.

Also check out the Least Common Multiple of 31872 and 31878