What is the Greatest Common Factor of 75123 and 75140?

Greatest common factor (GCF) of 75123 and 75140 is 17.

GCF(75123,75140) = 17

We will now calculate the prime factors of 75123 and 75140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75123 and 75140.

How to find the GCF of 75123 and 75140?

We will first find the prime factorization of 75123 and 75140. After we will calculate the factors of 75123 and 75140 and find the biggest common factor number .

Step-1: Prime Factorization of 75123

Prime factors of 75123 are 3, 17, 491. Prime factorization of 75123 in exponential form is:

75123 = 3² × 17¹ × 491¹

Step-2: Prime Factorization of 75140

Prime factors of 75140 are 2, 5, 13, 17. Prime factorization of 75140 in exponential form is:

75140 = 2² × 5¹ × 13¹ × 17²

Step-3: Factors of 75123

List of positive integer factors of 75123 that divides 75123 without a remainder.

1, 3, 9, 17, 51, 153, 491, 1473, 4419, 8347, 25041

Step-4: Factors of 75140

List of positive integer factors of 75140 that divides 75123 without a remainder.

1, 2, 4, 5, 10, 13, 17, 20, 26, 34, 52, 65, 68, 85, 130, 170, 221, 260, 289, 340, 442, 578, 884, 1105, 1156, 1445, 2210, 2890, 3757, 4420, 5780, 7514, 15028, 18785, 37570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75123 and 75140. The biggest common factor number is the GCF number.
So the greatest common factor 75123 and 75140 is 17.

Also check out the Least Common Multiple of 75123 and 75140