What is the Greatest Common Factor of 20609 and 20625?

Greatest common factor (GCF) of 20609 and 20625 is 1.

GCF(20609,20625) = 1

We will now calculate the prime factors of 20609 and 20625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20609 and 20625.

How to find the GCF of 20609 and 20625?

We will first find the prime factorization of 20609 and 20625. After we will calculate the factors of 20609 and 20625 and find the biggest common factor number .

Step-1: Prime Factorization of 20609

Prime factors of 20609 are 37, 557. Prime factorization of 20609 in exponential form is:

20609 = 37¹ × 557¹

Step-2: Prime Factorization of 20625

Prime factors of 20625 are 3, 5, 11. Prime factorization of 20625 in exponential form is:

20625 = 3¹ × 5⁴ × 11¹

Step-3: Factors of 20609

List of positive integer factors of 20609 that divides 20609 without a remainder.

1, 37, 557

Step-4: Factors of 20625

List of positive integer factors of 20625 that divides 20609 without a remainder.

1, 3, 5, 11, 15, 25, 33, 55, 75, 125, 165, 275, 375, 625, 825, 1375, 1875, 4125, 6875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20609 and 20625. The biggest common factor number is the GCF number.
So the greatest common factor 20609 and 20625 is 1.

Also check out the Least Common Multiple of 20609 and 20625