What is the Greatest Common Factor of 75213 and 75225?

Greatest common factor (GCF) of 75213 and 75225 is 3.

GCF(75213,75225) = 3

We will now calculate the prime factors of 75213 and 75225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75213 and 75225.

How to find the GCF of 75213 and 75225?

We will first find the prime factorization of 75213 and 75225. After we will calculate the factors of 75213 and 75225 and find the biggest common factor number .

Step-1: Prime Factorization of 75213

Prime factors of 75213 are 3, 61, 137. Prime factorization of 75213 in exponential form is:

75213 = 3² × 61¹ × 137¹

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 75213

List of positive integer factors of 75213 that divides 75213 without a remainder.

1, 3, 9, 61, 137, 183, 411, 549, 1233, 8357, 25071

Step-4: Factors of 75225

List of positive integer factors of 75225 that divides 75213 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 75213 and 75225. The biggest common factor number is the GCF number.
So the greatest common factor 75213 and 75225 is 3.

Also check out the Least Common Multiple of 75213 and 75225