What is the Greatest Common Factor of 21725 and 21740?

Greatest common factor (GCF) of 21725 and 21740 is 5.

GCF(21725,21740) = 5

We will now calculate the prime factors of 21725 and 21740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21725 and 21740.

How to find the GCF of 21725 and 21740?

We will first find the prime factorization of 21725 and 21740. After we will calculate the factors of 21725 and 21740 and find the biggest common factor number .

Step-1: Prime Factorization of 21725

Prime factors of 21725 are 5, 11, 79. Prime factorization of 21725 in exponential form is:

21725 = 5² × 11¹ × 79¹

Step-2: Prime Factorization of 21740

Prime factors of 21740 are 2, 5, 1087. Prime factorization of 21740 in exponential form is:

21740 = 2² × 5¹ × 1087¹

Step-3: Factors of 21725

List of positive integer factors of 21725 that divides 21725 without a remainder.

1, 5, 11, 25, 55, 79, 275, 395, 869, 1975, 4345

Step-4: Factors of 21740

List of positive integer factors of 21740 that divides 21725 without a remainder.

1, 2, 4, 5, 10, 20, 1087, 2174, 4348, 5435, 10870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21725 and 21740. The biggest common factor number is the GCF number.
So the greatest common factor 21725 and 21740 is 5.

Also check out the Least Common Multiple of 21725 and 21740