What is the Greatest Common Factor of 38625 and 38645?

Greatest common factor (GCF) of 38625 and 38645 is 5.

GCF(38625,38645) = 5

We will now calculate the prime factors of 38625 and 38645, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38625 and 38645.

How to find the GCF of 38625 and 38645?

We will first find the prime factorization of 38625 and 38645. After we will calculate the factors of 38625 and 38645 and find the biggest common factor number .

Step-1: Prime Factorization of 38625

Prime factors of 38625 are 3, 5, 103. Prime factorization of 38625 in exponential form is:

38625 = 3¹ × 5³ × 103¹

Step-2: Prime Factorization of 38645

Prime factors of 38645 are 5, 59, 131. Prime factorization of 38645 in exponential form is:

38645 = 5¹ × 59¹ × 131¹

Step-3: Factors of 38625

List of positive integer factors of 38625 that divides 38625 without a remainder.

1, 3, 5, 15, 25, 75, 103, 125, 309, 375, 515, 1545, 2575, 7725, 12875

Step-4: Factors of 38645

List of positive integer factors of 38645 that divides 38625 without a remainder.

1, 5, 59, 131, 295, 655, 7729

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38625 and 38645. The biggest common factor number is the GCF number.
So the greatest common factor 38625 and 38645 is 5.

Also check out the Least Common Multiple of 38625 and 38645