What is the Greatest Common Factor of 37653 and 37664?

Greatest common factor (GCF) of 37653 and 37664 is 11.

GCF(37653,37664) = 11

We will now calculate the prime factors of 37653 and 37664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37653 and 37664.

How to find the GCF of 37653 and 37664?

We will first find the prime factorization of 37653 and 37664. After we will calculate the factors of 37653 and 37664 and find the biggest common factor number .

Step-1: Prime Factorization of 37653

Prime factors of 37653 are 3, 7, 11, 163. Prime factorization of 37653 in exponential form is:

37653 = 3¹ × 7¹ × 11¹ × 163¹

Step-2: Prime Factorization of 37664

Prime factors of 37664 are 2, 11, 107. Prime factorization of 37664 in exponential form is:

37664 = 2⁵ × 11¹ × 107¹

Step-3: Factors of 37653

List of positive integer factors of 37653 that divides 37653 without a remainder.

1, 3, 7, 11, 21, 33, 77, 163, 231, 489, 1141, 1793, 3423, 5379, 12551

Step-4: Factors of 37664

List of positive integer factors of 37664 that divides 37653 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 107, 176, 214, 352, 428, 856, 1177, 1712, 2354, 3424, 4708, 9416, 18832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37653 and 37664. The biggest common factor number is the GCF number.
So the greatest common factor 37653 and 37664 is 11.

Also check out the Least Common Multiple of 37653 and 37664