What is the Greatest Common Factor of 75210 and 75216?

Greatest common factor (GCF) of 75210 and 75216 is 6.

GCF(75210,75216) = 6

We will now calculate the prime factors of 75210 and 75216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75210 and 75216.

How to find the GCF of 75210 and 75216?

We will first find the prime factorization of 75210 and 75216. After we will calculate the factors of 75210 and 75216 and find the biggest common factor number .

Step-1: Prime Factorization of 75210

Prime factors of 75210 are 2, 3, 5, 23, 109. Prime factorization of 75210 in exponential form is:

75210 = 2¹ × 3¹ × 5¹ × 23¹ × 109¹

Step-2: 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-3: Factors of 75210

List of positive integer factors of 75210 that divides 75210 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 109, 115, 138, 218, 230, 327, 345, 545, 654, 690, 1090, 1635, 2507, 3270, 5014, 7521, 12535, 15042, 25070, 37605

Step-4: Factors of 75216

List of positive integer factors of 75216 that divides 75210 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75210 and 75216. The biggest common factor number is the GCF number.
So the greatest common factor 75210 and 75216 is 6.

Also check out the Least Common Multiple of 75210 and 75216