What is the Greatest Common Factor of 25605 and 25625?

Greatest common factor (GCF) of 25605 and 25625 is 5.

GCF(25605,25625) = 5

We will now calculate the prime factors of 25605 and 25625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25605 and 25625.

How to find the GCF of 25605 and 25625?

We will first find the prime factorization of 25605 and 25625. After we will calculate the factors of 25605 and 25625 and find the biggest common factor number .

Step-1: Prime Factorization of 25605

Prime factors of 25605 are 3, 5, 569. Prime factorization of 25605 in exponential form is:

25605 = 3² × 5¹ × 569¹

Step-2: Prime Factorization of 25625

Prime factors of 25625 are 5, 41. Prime factorization of 25625 in exponential form is:

25625 = 5⁴ × 41¹

Step-3: Factors of 25605

List of positive integer factors of 25605 that divides 25605 without a remainder.

1, 3, 5, 9, 15, 45, 569, 1707, 2845, 5121, 8535

Step-4: Factors of 25625

List of positive integer factors of 25625 that divides 25605 without a remainder.

1, 5, 25, 41, 125, 205, 625, 1025, 5125

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25605 and 25625. The biggest common factor number is the GCF number.
So the greatest common factor 25605 and 25625 is 5.

Also check out the Least Common Multiple of 25605 and 25625