What is the Greatest Common Factor of 75210 and 75230?

Greatest common factor (GCF) of 75210 and 75230 is 10.

GCF(75210,75230) = 10

We will now calculate the prime factors of 75210 and 75230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75210 and 75230.

How to find the GCF of 75210 and 75230?

We will first find the prime factorization of 75210 and 75230. After we will calculate the factors of 75210 and 75230 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 75230

Prime factors of 75230 are 2, 5, 7523. Prime factorization of 75230 in exponential form is:

75230 = 2¹ × 5¹ × 7523¹

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 75230

List of positive integer factors of 75230 that divides 75210 without a remainder.

1, 2, 5, 10, 7523, 15046, 37615

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75210 and 75230. The biggest common factor number is the GCF number.
So the greatest common factor 75210 and 75230 is 10.

Also check out the Least Common Multiple of 75210 and 75230