What is the Greatest Common Factor of 38625 and 38643?

Greatest common factor (GCF) of 38625 and 38643 is 3.

GCF(38625,38643) = 3

We will now calculate the prime factors of 38625 and 38643, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38625 and 38643.

How to find the GCF of 38625 and 38643?

We will first find the prime factorization of 38625 and 38643. After we will calculate the factors of 38625 and 38643 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 38643

Prime factors of 38643 are 3, 11, 1171. Prime factorization of 38643 in exponential form is:

38643 = 3¹ × 11¹ × 1171¹

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 38643

List of positive integer factors of 38643 that divides 38625 without a remainder.

1, 3, 11, 33, 1171, 3513, 12881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38625 and 38643. The biggest common factor number is the GCF number.
So the greatest common factor 38625 and 38643 is 3.

Also check out the Least Common Multiple of 38625 and 38643