What is the Greatest Common Factor of 75632 and 75648?

Greatest common factor (GCF) of 75632 and 75648 is 16.

GCF(75632,75648) = 16

We will now calculate the prime factors of 75632 and 75648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75632 and 75648.

How to find the GCF of 75632 and 75648?

We will first find the prime factorization of 75632 and 75648. After we will calculate the factors of 75632 and 75648 and find the biggest common factor number .

Step-1: Prime Factorization of 75632

Prime factors of 75632 are 2, 29, 163. Prime factorization of 75632 in exponential form is:

75632 = 2⁴ × 29¹ × 163¹

Step-2: 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-3: Factors of 75632

List of positive integer factors of 75632 that divides 75632 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 163, 232, 326, 464, 652, 1304, 2608, 4727, 9454, 18908, 37816

Step-4: Factors of 75648

List of positive integer factors of 75648 that divides 75632 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75632 and 75648. The biggest common factor number is the GCF number.
So the greatest common factor 75632 and 75648 is 16.

Also check out the Least Common Multiple of 75632 and 75648