What is the Greatest Common Factor of 13125 and 13140?

Greatest common factor (GCF) of 13125 and 13140 is 15.

GCF(13125,13140) = 15

We will now calculate the prime factors of 13125 and 13140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13125 and 13140.

How to find the GCF of 13125 and 13140?

We will first find the prime factorization of 13125 and 13140. After we will calculate the factors of 13125 and 13140 and find the biggest common factor number .

Step-1: Prime Factorization of 13125

Prime factors of 13125 are 3, 5, 7. Prime factorization of 13125 in exponential form is:

13125 = 3¹ × 5⁴ × 7¹

Step-2: Prime Factorization of 13140

Prime factors of 13140 are 2, 3, 5, 73. Prime factorization of 13140 in exponential form is:

13140 = 2² × 3² × 5¹ × 73¹

Step-3: Factors of 13125

List of positive integer factors of 13125 that divides 13125 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 625, 875, 1875, 2625, 4375

Step-4: Factors of 13140

List of positive integer factors of 13140 that divides 13125 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 73, 90, 146, 180, 219, 292, 365, 438, 657, 730, 876, 1095, 1314, 1460, 2190, 2628, 3285, 4380, 6570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13125 and 13140. The biggest common factor number is the GCF number.
So the greatest common factor 13125 and 13140 is 15.

Also check out the Least Common Multiple of 13125 and 13140