What is the Greatest Common Factor of 16125 and 16140?

Greatest common factor (GCF) of 16125 and 16140 is 15.

GCF(16125,16140) = 15

We will now calculate the prime factors of 16125 and 16140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16125 and 16140.

How to find the GCF of 16125 and 16140?

We will first find the prime factorization of 16125 and 16140. After we will calculate the factors of 16125 and 16140 and find the biggest common factor number .

Step-1: Prime Factorization of 16125

Prime factors of 16125 are 3, 5, 43. Prime factorization of 16125 in exponential form is:

16125 = 3¹ × 5³ × 43¹

Step-2: Prime Factorization of 16140

Prime factors of 16140 are 2, 3, 5, 269. Prime factorization of 16140 in exponential form is:

16140 = 2² × 3¹ × 5¹ × 269¹

Step-3: Factors of 16125

List of positive integer factors of 16125 that divides 16125 without a remainder.

1, 3, 5, 15, 25, 43, 75, 125, 129, 215, 375, 645, 1075, 3225, 5375

Step-4: Factors of 16140

List of positive integer factors of 16140 that divides 16125 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 269, 538, 807, 1076, 1345, 1614, 2690, 3228, 4035, 5380, 8070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16125 and 16140. The biggest common factor number is the GCF number.
So the greatest common factor 16125 and 16140 is 15.

Also check out the Least Common Multiple of 16125 and 16140