What is the Greatest Common Factor of 75320 and 75328?

Greatest common factor (GCF) of 75320 and 75328 is 8.

GCF(75320,75328) = 8

We will now calculate the prime factors of 75320 and 75328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75320 and 75328.

How to find the GCF of 75320 and 75328?

We will first find the prime factorization of 75320 and 75328. After we will calculate the factors of 75320 and 75328 and find the biggest common factor number .

Step-1: Prime Factorization of 75320

Prime factors of 75320 are 2, 5, 7, 269. Prime factorization of 75320 in exponential form is:

75320 = 2³ × 5¹ × 7¹ × 269¹

Step-2: Prime Factorization of 75328

Prime factors of 75328 are 2, 11, 107. Prime factorization of 75328 in exponential form is:

75328 = 2⁶ × 11¹ × 107¹

Step-3: Factors of 75320

List of positive integer factors of 75320 that divides 75320 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 269, 280, 538, 1076, 1345, 1883, 2152, 2690, 3766, 5380, 7532, 9415, 10760, 15064, 18830, 37660

Step-4: Factors of 75328

List of positive integer factors of 75328 that divides 75320 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 107, 176, 214, 352, 428, 704, 856, 1177, 1712, 2354, 3424, 4708, 6848, 9416, 18832, 37664

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75320 and 75328. The biggest common factor number is the GCF number.
So the greatest common factor 75320 and 75328 is 8.

Also check out the Least Common Multiple of 75320 and 75328