What is the Greatest Common Factor of 13625 and 13630?

Greatest common factor (GCF) of 13625 and 13630 is 5.

GCF(13625,13630) = 5

We will now calculate the prime factors of 13625 and 13630, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13625 and 13630.

How to find the GCF of 13625 and 13630?

We will first find the prime factorization of 13625 and 13630. After we will calculate the factors of 13625 and 13630 and find the biggest common factor number .

Step-1: Prime Factorization of 13625

Prime factors of 13625 are 5, 109. Prime factorization of 13625 in exponential form is:

13625 = 5³ × 109¹

Step-2: Prime Factorization of 13630

Prime factors of 13630 are 2, 5, 29, 47. Prime factorization of 13630 in exponential form is:

13630 = 2¹ × 5¹ × 29¹ × 47¹

Step-3: Factors of 13625

List of positive integer factors of 13625 that divides 13625 without a remainder.

1, 5, 25, 109, 125, 545, 2725

Step-4: Factors of 13630

List of positive integer factors of 13630 that divides 13625 without a remainder.

1, 2, 5, 10, 29, 47, 58, 94, 145, 235, 290, 470, 1363, 2726, 6815

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13625 and 13630. The biggest common factor number is the GCF number.
So the greatest common factor 13625 and 13630 is 5.

Also check out the Least Common Multiple of 13625 and 13630