What is the Greatest Common Factor of 10125 and 10140?

Greatest common factor (GCF) of 10125 and 10140 is 15.

GCF(10125,10140) = 15

We will now calculate the prime factors of 10125 and 10140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10125 and 10140.

How to find the GCF of 10125 and 10140?

We will first find the prime factorization of 10125 and 10140. After we will calculate the factors of 10125 and 10140 and find the biggest common factor number .

Step-1: Prime Factorization of 10125

Prime factors of 10125 are 3, 5. Prime factorization of 10125 in exponential form is:

10125 = 3⁴ × 5³

Step-2: Prime Factorization of 10140

Prime factors of 10140 are 2, 3, 5, 13. Prime factorization of 10140 in exponential form is:

10140 = 2² × 3¹ × 5¹ × 13²

Step-3: Factors of 10125

List of positive integer factors of 10125 that divides 10125 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 375, 405, 675, 1125, 2025, 3375

Step-4: Factors of 10140

List of positive integer factors of 10140 that divides 10125 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 169, 195, 260, 338, 390, 507, 676, 780, 845, 1014, 1690, 2028, 2535, 3380, 5070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10125 and 10140. The biggest common factor number is the GCF number.
So the greatest common factor 10125 and 10140 is 15.

Also check out the Least Common Multiple of 10125 and 10140