What is the Greatest Common Factor of 37128 and 37140?

Greatest common factor (GCF) of 37128 and 37140 is 12.

GCF(37128,37140) = 12

We will now calculate the prime factors of 37128 and 37140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37128 and 37140.

How to find the GCF of 37128 and 37140?

We will first find the prime factorization of 37128 and 37140. After we will calculate the factors of 37128 and 37140 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 37140

Prime factors of 37140 are 2, 3, 5, 619. Prime factorization of 37140 in exponential form is:

37140 = 2² × 3¹ × 5¹ × 619¹

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 37140

List of positive integer factors of 37140 that divides 37128 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 619, 1238, 1857, 2476, 3095, 3714, 6190, 7428, 9285, 12380, 18570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37128 and 37140. The biggest common factor number is the GCF number.
So the greatest common factor 37128 and 37140 is 12.

Also check out the Least Common Multiple of 37128 and 37140