What is the Greatest Common Factor of 31374 and 31392?

Greatest common factor (GCF) of 31374 and 31392 is 18.

GCF(31374,31392) = 18

We will now calculate the prime factors of 31374 and 31392, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31374 and 31392.

How to find the GCF of 31374 and 31392?

We will first find the prime factorization of 31374 and 31392. After we will calculate the factors of 31374 and 31392 and find the biggest common factor number .

Step-1: Prime Factorization of 31374

Prime factors of 31374 are 2, 3, 7, 83. Prime factorization of 31374 in exponential form is:

31374 = 2¹ × 3³ × 7¹ × 83¹

Step-2: Prime Factorization of 31392

Prime factors of 31392 are 2, 3, 109. Prime factorization of 31392 in exponential form is:

31392 = 2⁵ × 3² × 109¹

Step-3: Factors of 31374

List of positive integer factors of 31374 that divides 31374 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 83, 126, 166, 189, 249, 378, 498, 581, 747, 1162, 1494, 1743, 2241, 3486, 4482, 5229, 10458, 15687

Step-4: Factors of 31392

List of positive integer factors of 31392 that divides 31374 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 109, 144, 218, 288, 327, 436, 654, 872, 981, 1308, 1744, 1962, 2616, 3488, 3924, 5232, 7848, 10464, 15696

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31374 and 31392. The biggest common factor number is the GCF number.
So the greatest common factor 31374 and 31392 is 18.

Also check out the Least Common Multiple of 31374 and 31392