What is the Greatest Common Factor of 21605 and 21625?

Greatest common factor (GCF) of 21605 and 21625 is 5.

GCF(21605,21625) = 5

We will now calculate the prime factors of 21605 and 21625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21605 and 21625.

How to find the GCF of 21605 and 21625?

We will first find the prime factorization of 21605 and 21625. After we will calculate the factors of 21605 and 21625 and find the biggest common factor number .

Step-1: Prime Factorization of 21605

Prime factors of 21605 are 5, 29, 149. Prime factorization of 21605 in exponential form is:

21605 = 5¹ × 29¹ × 149¹

Step-2: Prime Factorization of 21625

Prime factors of 21625 are 5, 173. Prime factorization of 21625 in exponential form is:

21625 = 5³ × 173¹

Step-3: Factors of 21605

List of positive integer factors of 21605 that divides 21605 without a remainder.

1, 5, 29, 145, 149, 745, 4321

Step-4: Factors of 21625

List of positive integer factors of 21625 that divides 21605 without a remainder.

1, 5, 25, 125, 173, 865, 4325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21605 and 21625. The biggest common factor number is the GCF number.
So the greatest common factor 21605 and 21625 is 5.

Also check out the Least Common Multiple of 21605 and 21625