What is the Greatest Common Factor of 67644 and 67664?

Greatest common factor (GCF) of 67644 and 67664 is 4.

GCF(67644,67664) = 4

We will now calculate the prime factors of 67644 and 67664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67644 and 67664.

How to find the GCF of 67644 and 67664?

We will first find the prime factorization of 67644 and 67664. After we will calculate the factors of 67644 and 67664 and find the biggest common factor number .

Step-1: Prime Factorization of 67644

Prime factors of 67644 are 2, 3, 1879. Prime factorization of 67644 in exponential form is:

67644 = 2² × 3² × 1879¹

Step-2: Prime Factorization of 67664

Prime factors of 67664 are 2, 4229. Prime factorization of 67664 in exponential form is:

67664 = 2⁴ × 4229¹

Step-3: Factors of 67644

List of positive integer factors of 67644 that divides 67644 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 1879, 3758, 5637, 7516, 11274, 16911, 22548, 33822

Step-4: Factors of 67664

List of positive integer factors of 67664 that divides 67644 without a remainder.

1, 2, 4, 8, 16, 4229, 8458, 16916, 33832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67644 and 67664. The biggest common factor number is the GCF number.
So the greatest common factor 67644 and 67664 is 4.

Also check out the Least Common Multiple of 67644 and 67664