What is the Greatest Common Factor of 75314 and 75328?

Greatest common factor (GCF) of 75314 and 75328 is 2.

GCF(75314,75328) = 2

We will now calculate the prime factors of 75314 and 75328, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75314 and 75328.

How to find the GCF of 75314 and 75328?

We will first find the prime factorization of 75314 and 75328. After we will calculate the factors of 75314 and 75328 and find the biggest common factor number .

Step-1: Prime Factorization of 75314

Prime factors of 75314 are 2, 37657. Prime factorization of 75314 in exponential form is:

75314 = 2¹ × 37657¹

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 75314

List of positive integer factors of 75314 that divides 75314 without a remainder.

1, 2, 37657

Step-4: Factors of 75328

List of positive integer factors of 75328 that divides 75314 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 75314 and 75328. The biggest common factor number is the GCF number.
So the greatest common factor 75314 and 75328 is 2.

Also check out the Least Common Multiple of 75314 and 75328