What is the Greatest Common Factor of 75648 and 75664?

Greatest common factor (GCF) of 75648 and 75664 is 16.

GCF(75648,75664) = 16

We will now calculate the prime factors of 75648 and 75664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75648 and 75664.

How to find the GCF of 75648 and 75664?

We will first find the prime factorization of 75648 and 75664. After we will calculate the factors of 75648 and 75664 and find the biggest common factor number .

Step-1: Prime Factorization of 75648

Prime factors of 75648 are 2, 3, 197. Prime factorization of 75648 in exponential form is:

75648 = 2⁷ × 3¹ × 197¹

Step-2: Prime Factorization of 75664

Prime factors of 75664 are 2, 4729. Prime factorization of 75664 in exponential form is:

75664 = 2⁴ × 4729¹

Step-3: Factors of 75648

List of positive integer factors of 75648 that divides 75648 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 197, 384, 394, 591, 788, 1182, 1576, 2364, 3152, 4728, 6304, 9456, 12608, 18912, 25216, 37824

Step-4: Factors of 75664

List of positive integer factors of 75664 that divides 75648 without a remainder.

1, 2, 4, 8, 16, 4729, 9458, 18916, 37832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75648 and 75664. The biggest common factor number is the GCF number.
So the greatest common factor 75648 and 75664 is 16.

Also check out the Least Common Multiple of 75648 and 75664