What is the Greatest Common Factor of 37536 and 37542?

Greatest common factor (GCF) of 37536 and 37542 is 6.

GCF(37536,37542) = 6

We will now calculate the prime factors of 37536 and 37542, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37536 and 37542.

How to find the GCF of 37536 and 37542?

We will first find the prime factorization of 37536 and 37542. After we will calculate the factors of 37536 and 37542 and find the biggest common factor number .

Step-1: Prime Factorization of 37536

Prime factors of 37536 are 2, 3, 17, 23. Prime factorization of 37536 in exponential form is:

37536 = 2⁵ × 3¹ × 17¹ × 23¹

Step-2: Prime Factorization of 37542

Prime factors of 37542 are 2, 3, 6257. Prime factorization of 37542 in exponential form is:

37542 = 2¹ × 3¹ × 6257¹

Step-3: Factors of 37536

List of positive integer factors of 37536 that divides 37536 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 23, 24, 32, 34, 46, 48, 51, 68, 69, 92, 96, 102, 136, 138, 184, 204, 272, 276, 368, 391, 408, 544, 552, 736, 782, 816, 1104, 1173, 1564, 1632, 2208, 2346, 3128, 4692, 6256, 9384, 12512, 18768

Step-4: Factors of 37542

List of positive integer factors of 37542 that divides 37536 without a remainder.

1, 2, 3, 6, 6257, 12514, 18771

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37536 and 37542. The biggest common factor number is the GCF number.
So the greatest common factor 37536 and 37542 is 6.

Also check out the Least Common Multiple of 37536 and 37542