What is the Greatest Common Factor of 37519 and 37536?

Greatest common factor (GCF) of 37519 and 37536 is 17.

GCF(37519,37536) = 17

We will now calculate the prime factors of 37519 and 37536, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37519 and 37536.

How to find the GCF of 37519 and 37536?

We will first find the prime factorization of 37519 and 37536. After we will calculate the factors of 37519 and 37536 and find the biggest common factor number .

Step-1: Prime Factorization of 37519

Prime factors of 37519 are 17, 2207. Prime factorization of 37519 in exponential form is:

37519 = 17¹ × 2207¹

Step-2: 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-3: Factors of 37519

List of positive integer factors of 37519 that divides 37519 without a remainder.

1, 17, 2207

Step-4: Factors of 37536

List of positive integer factors of 37536 that divides 37519 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37519 and 37536. The biggest common factor number is the GCF number.
So the greatest common factor 37519 and 37536 is 17.

Also check out the Least Common Multiple of 37519 and 37536