What is the Greatest Common Factor of 625 and 638?

Greatest common factor (GCF) of 625 and 638 is 1.

GCF(625,638) = 1

We will now calculate the prime factors of 625 and 638, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 625 and 638.

How to find the GCF of 625 and 638?

We will first find the prime factorization of 625 and 638. After we will calculate the factors of 625 and 638 and find the biggest common factor number .

Step-1: Prime Factorization of 625

Prime factors of 625 are 5. Prime factorization of 625 in exponential form is:

625 = 5⁴

Step-2: Prime Factorization of 638

Prime factors of 638 are 2, 11, 29. Prime factorization of 638 in exponential form is:

638 = 2¹ × 11¹ × 29¹

Step-3: Factors of 625

List of positive integer factors of 625 that divides 625 without a remainder.

1, 5, 25, 125

Step-4: Factors of 638

List of positive integer factors of 638 that divides 625 without a remainder.

1, 2, 11, 22, 29, 58, 319

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 625 and 638. The biggest common factor number is the GCF number.
So the greatest common factor 625 and 638 is 1.

Also check out the Least Common Multiple of 625 and 638