What is the Greatest Common Factor of 75140 and 75150?

Greatest common factor (GCF) of 75140 and 75150 is 10.

GCF(75140,75150) = 10

We will now calculate the prime factors of 75140 and 75150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75140 and 75150.

How to find the GCF of 75140 and 75150?

We will first find the prime factorization of 75140 and 75150. After we will calculate the factors of 75140 and 75150 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75150

Prime factors of 75150 are 2, 3, 5, 167. Prime factorization of 75150 in exponential form is:

75150 = 2¹ × 3² × 5² × 167¹

Step-3: Factors of 75140

List of positive integer factors of 75140 that divides 75140 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

Step-4: Factors of 75150

List of positive integer factors of 75150 that divides 75140 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 167, 225, 334, 450, 501, 835, 1002, 1503, 1670, 2505, 3006, 4175, 5010, 7515, 8350, 12525, 15030, 25050, 37575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75140 and 75150. The biggest common factor number is the GCF number.
So the greatest common factor 75140 and 75150 is 10.

Also check out the Least Common Multiple of 75140 and 75150