What is the Greatest Common Factor of 3642 and 3648?

Greatest common factor (GCF) of 3642 and 3648 is 6.

GCF(3642,3648) = 6

We will now calculate the prime factors of 3642 and 3648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3642 and 3648.

How to find the GCF of 3642 and 3648?

We will first find the prime factorization of 3642 and 3648. After we will calculate the factors of 3642 and 3648 and find the biggest common factor number .

Step-1: Prime Factorization of 3642

Prime factors of 3642 are 2, 3, 607. Prime factorization of 3642 in exponential form is:

3642 = 2¹ × 3¹ × 607¹

Step-2: 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-3: Factors of 3642

List of positive integer factors of 3642 that divides 3642 without a remainder.

1, 2, 3, 6, 607, 1214, 1821

Step-4: Factors of 3648

List of positive integer factors of 3648 that divides 3642 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3642 and 3648. The biggest common factor number is the GCF number.
So the greatest common factor 3642 and 3648 is 6.

Also check out the Least Common Multiple of 3642 and 3648