What is the Greatest Common Factor of 37128 and 37144?

Greatest common factor (GCF) of 37128 and 37144 is 8.

GCF(37128,37144) = 8

We will now calculate the prime factors of 37128 and 37144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37128 and 37144.

How to find the GCF of 37128 and 37144?

We will first find the prime factorization of 37128 and 37144. After we will calculate the factors of 37128 and 37144 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 37144

Prime factors of 37144 are 2, 4643. Prime factorization of 37144 in exponential form is:

37144 = 2³ × 4643¹

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 37144

List of positive integer factors of 37144 that divides 37128 without a remainder.

1, 2, 4, 8, 4643, 9286, 18572

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37128 and 37144. The biggest common factor number is the GCF number.
So the greatest common factor 37128 and 37144 is 8.

Also check out the Least Common Multiple of 37128 and 37144