What is the Greatest Common Factor of 3648 and 3654?

Greatest common factor (GCF) of 3648 and 3654 is 6.

GCF(3648,3654) = 6

We will now calculate the prime factors of 3648 and 3654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3648 and 3654.

How to find the GCF of 3648 and 3654?

We will first find the prime factorization of 3648 and 3654. After we will calculate the factors of 3648 and 3654 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 3654

Prime factors of 3654 are 2, 3, 7, 29. Prime factorization of 3654 in exponential form is:

3654 = 2¹ × 3² × 7¹ × 29¹

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 3654

List of positive integer factors of 3654 that divides 3648 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 29, 42, 58, 63, 87, 126, 174, 203, 261, 406, 522, 609, 1218, 1827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3648 and 3654. The biggest common factor number is the GCF number.
So the greatest common factor 3648 and 3654 is 6.

Also check out the Least Common Multiple of 3648 and 3654