What is the Greatest Common Factor of 31878 and 31892?

Greatest common factor (GCF) of 31878 and 31892 is 14.

GCF(31878,31892) = 14

We will now calculate the prime factors of 31878 and 31892, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31878 and 31892.

How to find the GCF of 31878 and 31892?

We will first find the prime factorization of 31878 and 31892. After we will calculate the factors of 31878 and 31892 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31892

Prime factors of 31892 are 2, 7, 17, 67. Prime factorization of 31892 in exponential form is:

31892 = 2² × 7¹ × 17¹ × 67¹

Step-3: Factors of 31878

List of positive integer factors of 31878 that divides 31878 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

Step-4: Factors of 31892

List of positive integer factors of 31892 that divides 31878 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 67, 68, 119, 134, 238, 268, 469, 476, 938, 1139, 1876, 2278, 4556, 7973, 15946

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31878 and 31892. The biggest common factor number is the GCF number.
So the greatest common factor 31878 and 31892 is 14.

Also check out the Least Common Multiple of 31878 and 31892