What is the Greatest Common Factor of 75216 and 75234?

Greatest common factor (GCF) of 75216 and 75234 is 6.

GCF(75216,75234) = 6

We will now calculate the prime factors of 75216 and 75234, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75216 and 75234.

How to find the GCF of 75216 and 75234?

We will first find the prime factorization of 75216 and 75234. After we will calculate the factors of 75216 and 75234 and find the biggest common factor number .

Step-1: Prime Factorization of 75216

Prime factors of 75216 are 2, 3, 1567. Prime factorization of 75216 in exponential form is:

75216 = 2⁴ × 3¹ × 1567¹

Step-2: Prime Factorization of 75234

Prime factors of 75234 are 2, 3, 12539. Prime factorization of 75234 in exponential form is:

75234 = 2¹ × 3¹ × 12539¹

Step-3: Factors of 75216

List of positive integer factors of 75216 that divides 75216 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1567, 3134, 4701, 6268, 9402, 12536, 18804, 25072, 37608

Step-4: Factors of 75234

List of positive integer factors of 75234 that divides 75216 without a remainder.

1, 2, 3, 6, 12539, 25078, 37617

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75216 and 75234. The biggest common factor number is the GCF number.
So the greatest common factor 75216 and 75234 is 6.

Also check out the Least Common Multiple of 75216 and 75234