What is the Greatest Common Factor of 3634 and 3648?

Greatest common factor (GCF) of 3634 and 3648 is 2.

GCF(3634,3648) = 2

We will now calculate the prime factors of 3634 and 3648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3634 and 3648.

How to find the GCF of 3634 and 3648?

We will first find the prime factorization of 3634 and 3648. After we will calculate the factors of 3634 and 3648 and find the biggest common factor number .

Step-1: Prime Factorization of 3634

Prime factors of 3634 are 2, 23, 79. Prime factorization of 3634 in exponential form is:

3634 = 2¹ × 23¹ × 79¹

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 3634

List of positive integer factors of 3634 that divides 3634 without a remainder.

1, 2, 23, 46, 79, 158, 1817

Step-4: Factors of 3648

List of positive integer factors of 3648 that divides 3634 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 3634 and 3648. The biggest common factor number is the GCF number.
So the greatest common factor 3634 and 3648 is 2.

Also check out the Least Common Multiple of 3634 and 3648