What is the Greatest Common Factor of 21609 and 21623?

Greatest common factor (GCF) of 21609 and 21623 is 7.

GCF(21609,21623) = 7

We will now calculate the prime factors of 21609 and 21623, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21609 and 21623.

How to find the GCF of 21609 and 21623?

We will first find the prime factorization of 21609 and 21623. After we will calculate the factors of 21609 and 21623 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 21623

Prime factors of 21623 are 7, 3089. Prime factorization of 21623 in exponential form is:

21623 = 7¹ × 3089¹

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 21623

List of positive integer factors of 21623 that divides 21609 without a remainder.

1, 7, 3089

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21609 and 21623. The biggest common factor number is the GCF number.
So the greatest common factor 21609 and 21623 is 7.

Also check out the Least Common Multiple of 21609 and 21623