What is the Greatest Common Factor of 75190 and 75210?

Greatest common factor (GCF) of 75190 and 75210 is 10.

GCF(75190,75210) = 10

We will now calculate the prime factors of 75190 and 75210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75190 and 75210.

How to find the GCF of 75190 and 75210?

We will first find the prime factorization of 75190 and 75210. After we will calculate the factors of 75190 and 75210 and find the biggest common factor number .

Step-1: Prime Factorization of 75190

Prime factors of 75190 are 2, 5, 73, 103. Prime factorization of 75190 in exponential form is:

75190 = 2¹ × 5¹ × 73¹ × 103¹

Step-2: 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-3: Factors of 75190

List of positive integer factors of 75190 that divides 75190 without a remainder.

1, 2, 5, 10, 73, 103, 146, 206, 365, 515, 730, 1030, 7519, 15038, 37595

Step-4: Factors of 75210

List of positive integer factors of 75210 that divides 75190 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75190 and 75210. The biggest common factor number is the GCF number.
So the greatest common factor 75190 and 75210 is 10.

Also check out the Least Common Multiple of 75190 and 75210