What is the Greatest Common Factor of 37119 and 37128?

Greatest common factor (GCF) of 37119 and 37128 is 3.

GCF(37119,37128) = 3

We will now calculate the prime factors of 37119 and 37128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37119 and 37128.

How to find the GCF of 37119 and 37128?

We will first find the prime factorization of 37119 and 37128. After we will calculate the factors of 37119 and 37128 and find the biggest common factor number .

Step-1: Prime Factorization of 37119

Prime factors of 37119 are 3, 12373. Prime factorization of 37119 in exponential form is:

37119 = 3¹ × 12373¹

Step-2: 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-3: Factors of 37119

List of positive integer factors of 37119 that divides 37119 without a remainder.

1, 3, 12373

Step-4: Factors of 37128

List of positive integer factors of 37128 that divides 37119 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37119 and 37128. The biggest common factor number is the GCF number.
So the greatest common factor 37119 and 37128 is 3.

Also check out the Least Common Multiple of 37119 and 37128