What is the Greatest Common Factor of 21609 and 21625?

Greatest common factor (GCF) of 21609 and 21625 is 1.

GCF(21609,21625) = 1

We will now calculate the prime factors of 21609 and 21625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21609 and 21625.

How to find the GCF of 21609 and 21625?

We will first find the prime factorization of 21609 and 21625. After we will calculate the factors of 21609 and 21625 and find the biggest common factor number .

Step-1: Prime Factorization of 21609

Prime factors of 21609 are 3, 7. Prime factorization of 21609 in exponential form is:

21609 = 3² × 7⁴

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 21609

List of positive integer factors of 21609 that divides 21609 without a remainder.

1, 3, 7, 9, 21, 49, 63, 147, 343, 441, 1029, 2401, 3087, 7203

Step-4: Factors of 21625

List of positive integer factors of 21625 that divides 21609 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21609 and 21625. The biggest common factor number is the GCF number.
So the greatest common factor 21609 and 21625 is 1.

Also check out the Least Common Multiple of 21609 and 21625