What is the Greatest Common Factor of 31878 and 31896?

Greatest common factor (GCF) of 31878 and 31896 is 18.

GCF(31878,31896) = 18

We will now calculate the prime factors of 31878 and 31896, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31878 and 31896.

How to find the GCF of 31878 and 31896?

We will first find the prime factorization of 31878 and 31896. After we will calculate the factors of 31878 and 31896 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 31896

Prime factors of 31896 are 2, 3, 443. Prime factorization of 31896 in exponential form is:

31896 = 2³ × 3² × 443¹

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 31896

List of positive integer factors of 31896 that divides 31878 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 443, 886, 1329, 1772, 2658, 3544, 3987, 5316, 7974, 10632, 15948

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31878 and 31896. The biggest common factor number is the GCF number.
So the greatest common factor 31878 and 31896 is 18.

Also check out the Least Common Multiple of 31878 and 31896