What is the Greatest Common Factor of 75314 and 75332?

Greatest common factor (GCF) of 75314 and 75332 is 2.

GCF(75314,75332) = 2

We will now calculate the prime factors of 75314 and 75332, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75314 and 75332.

How to find the GCF of 75314 and 75332?

We will first find the prime factorization of 75314 and 75332. After we will calculate the factors of 75314 and 75332 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 75332

Prime factors of 75332 are 2, 37, 509. Prime factorization of 75332 in exponential form is:

75332 = 2² × 37¹ × 509¹

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 75332

List of positive integer factors of 75332 that divides 75314 without a remainder.

1, 2, 4, 37, 74, 148, 509, 1018, 2036, 18833, 37666

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75314 and 75332. The biggest common factor number is the GCF number.
So the greatest common factor 75314 and 75332 is 2.

Also check out the Least Common Multiple of 75314 and 75332