What is the Greatest Common Factor of 3648 and 3667?

Greatest common factor (GCF) of 3648 and 3667 is 19.

GCF(3648,3667) = 19

We will now calculate the prime factors of 3648 and 3667, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3648 and 3667.

How to find the GCF of 3648 and 3667?

We will first find the prime factorization of 3648 and 3667. After we will calculate the factors of 3648 and 3667 and find the biggest common factor number .

Step-1: Prime Factorization of 3648

Prime factors of 3648 are 2, 3, 19. Prime factorization of 3648 in exponential form is:

3648 = 2⁶ × 3¹ × 19¹

Step-2: Prime Factorization of 3667

Prime factors of 3667 are 19, 193. Prime factorization of 3667 in exponential form is:

3667 = 19¹ × 193¹

Step-3: Factors of 3648

List of positive integer factors of 3648 that divides 3648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 456, 608, 912, 1216, 1824

Step-4: Factors of 3667

List of positive integer factors of 3667 that divides 3648 without a remainder.

1, 19, 193

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3648 and 3667. The biggest common factor number is the GCF number.
So the greatest common factor 3648 and 3667 is 19.

Also check out the Least Common Multiple of 3648 and 3667