What is the Greatest Common Factor of 21125 and 21138?

Greatest common factor (GCF) of 21125 and 21138 is 13.

GCF(21125,21138) = 13

We will now calculate the prime factors of 21125 and 21138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21125 and 21138.

How to find the GCF of 21125 and 21138?

We will first find the prime factorization of 21125 and 21138. After we will calculate the factors of 21125 and 21138 and find the biggest common factor number .

Step-1: Prime Factorization of 21125

Prime factors of 21125 are 5, 13. Prime factorization of 21125 in exponential form is:

21125 = 5³ × 13²

Step-2: Prime Factorization of 21138

Prime factors of 21138 are 2, 3, 13, 271. Prime factorization of 21138 in exponential form is:

21138 = 2¹ × 3¹ × 13¹ × 271¹

Step-3: Factors of 21125

List of positive integer factors of 21125 that divides 21125 without a remainder.

1, 5, 13, 25, 65, 125, 169, 325, 845, 1625, 4225

Step-4: Factors of 21138

List of positive integer factors of 21138 that divides 21125 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 271, 542, 813, 1626, 3523, 7046, 10569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21125 and 21138. The biggest common factor number is the GCF number.
So the greatest common factor 21125 and 21138 is 13.

Also check out the Least Common Multiple of 21125 and 21138