What is the Greatest Common Factor of 75648 and 75654?

Greatest common factor (GCF) of 75648 and 75654 is 6.

GCF(75648,75654) = 6

We will now calculate the prime factors of 75648 and 75654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75648 and 75654.

How to find the GCF of 75648 and 75654?

We will first find the prime factorization of 75648 and 75654. After we will calculate the factors of 75648 and 75654 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 75654

Prime factors of 75654 are 2, 3, 467. Prime factorization of 75654 in exponential form is:

75654 = 2¹ × 3⁴ × 467¹

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 75654

List of positive integer factors of 75654 that divides 75648 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 467, 934, 1401, 2802, 4203, 8406, 12609, 25218, 37827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75648 and 75654. The biggest common factor number is the GCF number.
So the greatest common factor 75648 and 75654 is 6.

Also check out the Least Common Multiple of 75648 and 75654