What is the Greatest Common Factor of 37128 and 37134?

Greatest common factor (GCF) of 37128 and 37134 is 6.

GCF(37128,37134) = 6

We will now calculate the prime factors of 37128 and 37134, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37128 and 37134.

How to find the GCF of 37128 and 37134?

We will first find the prime factorization of 37128 and 37134. After we will calculate the factors of 37128 and 37134 and find the biggest common factor number .

Step-1: Prime Factorization of 37128

Prime factors of 37128 are 2, 3, 7, 13, 17. Prime factorization of 37128 in exponential form is:

37128 = 2³ × 3¹ × 7¹ × 13¹ × 17¹

Step-2: Prime Factorization of 37134

Prime factors of 37134 are 2, 3, 2063. Prime factorization of 37134 in exponential form is:

37134 = 2¹ × 3² × 2063¹

Step-3: Factors of 37128

List of positive integer factors of 37128 that divides 37128 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 17, 21, 24, 26, 28, 34, 39, 42, 51, 52, 56, 68, 78, 84, 91, 102, 104, 119, 136, 156, 168, 182, 204, 221, 238, 273, 312, 357, 364, 408, 442, 476, 546, 663, 714, 728, 884, 952, 1092, 1326, 1428, 1547, 1768, 2184, 2652, 2856, 3094, 4641, 5304, 6188, 9282, 12376, 18564

Step-4: Factors of 37134

List of positive integer factors of 37134 that divides 37128 without a remainder.

1, 2, 3, 6, 9, 18, 2063, 4126, 6189, 12378, 18567

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37128 and 37134. The biggest common factor number is the GCF number.
So the greatest common factor 37128 and 37134 is 6.

Also check out the Least Common Multiple of 37128 and 37134