What is the Greatest Common Factor of 75216 and 75225?

Greatest common factor (GCF) of 75216 and 75225 is 3.

GCF(75216,75225) = 3

We will now calculate the prime factors of 75216 and 75225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75216 and 75225.

How to find the GCF of 75216 and 75225?

We will first find the prime factorization of 75216 and 75225. After we will calculate the factors of 75216 and 75225 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 75225

Prime factors of 75225 are 3, 5, 17, 59. Prime factorization of 75225 in exponential form is:

75225 = 3¹ × 5² × 17¹ × 59¹

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 75225

List of positive integer factors of 75225 that divides 75216 without a remainder.

1, 3, 5, 15, 17, 25, 51, 59, 75, 85, 177, 255, 295, 425, 885, 1003, 1275, 1475, 3009, 4425, 5015, 15045, 25075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75216 and 75225. The biggest common factor number is the GCF number.
So the greatest common factor 75216 and 75225 is 3.

Also check out the Least Common Multiple of 75216 and 75225