What is the Greatest Common Factor of 36744 and 36762?

Greatest common factor (GCF) of 36744 and 36762 is 6.

GCF(36744,36762) = 6

We will now calculate the prime factors of 36744 and 36762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36744 and 36762.

How to find the GCF of 36744 and 36762?

We will first find the prime factorization of 36744 and 36762. After we will calculate the factors of 36744 and 36762 and find the biggest common factor number .

Step-1: Prime Factorization of 36744

Prime factors of 36744 are 2, 3, 1531. Prime factorization of 36744 in exponential form is:

36744 = 2³ × 3¹ × 1531¹

Step-2: Prime Factorization of 36762

Prime factors of 36762 are 2, 3, 11, 557. Prime factorization of 36762 in exponential form is:

36762 = 2¹ × 3¹ × 11¹ × 557¹

Step-3: Factors of 36744

List of positive integer factors of 36744 that divides 36744 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 1531, 3062, 4593, 6124, 9186, 12248, 18372

Step-4: Factors of 36762

List of positive integer factors of 36762 that divides 36744 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 557, 1114, 1671, 3342, 6127, 12254, 18381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36744 and 36762. The biggest common factor number is the GCF number.
So the greatest common factor 36744 and 36762 is 6.

Also check out the Least Common Multiple of 36744 and 36762