What is the Greatest Common Factor of 43125 and 43140?

Greatest common factor (GCF) of 43125 and 43140 is 15.

GCF(43125,43140) = 15

We will now calculate the prime factors of 43125 and 43140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43125 and 43140.

How to find the GCF of 43125 and 43140?

We will first find the prime factorization of 43125 and 43140. After we will calculate the factors of 43125 and 43140 and find the biggest common factor number .

Step-1: Prime Factorization of 43125

Prime factors of 43125 are 3, 5, 23. Prime factorization of 43125 in exponential form is:

43125 = 3¹ × 5⁴ × 23¹

Step-2: Prime Factorization of 43140

Prime factors of 43140 are 2, 3, 5, 719. Prime factorization of 43140 in exponential form is:

43140 = 2² × 3¹ × 5¹ × 719¹

Step-3: Factors of 43125

List of positive integer factors of 43125 that divides 43125 without a remainder.

1, 3, 5, 15, 23, 25, 69, 75, 115, 125, 345, 375, 575, 625, 1725, 1875, 2875, 8625, 14375

Step-4: Factors of 43140

List of positive integer factors of 43140 that divides 43125 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 719, 1438, 2157, 2876, 3595, 4314, 7190, 8628, 10785, 14380, 21570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43125 and 43140. The biggest common factor number is the GCF number.
So the greatest common factor 43125 and 43140 is 15.

Also check out the Least Common Multiple of 43125 and 43140