What is the Greatest Common Factor of 17625 and 17634?

Greatest common factor (GCF) of 17625 and 17634 is 3.

GCF(17625,17634) = 3

We will now calculate the prime factors of 17625 and 17634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17625 and 17634.

How to find the GCF of 17625 and 17634?

We will first find the prime factorization of 17625 and 17634. After we will calculate the factors of 17625 and 17634 and find the biggest common factor number .

Step-1: Prime Factorization of 17625

Prime factors of 17625 are 3, 5, 47. Prime factorization of 17625 in exponential form is:

17625 = 3¹ × 5³ × 47¹

Step-2: Prime Factorization of 17634

Prime factors of 17634 are 2, 3, 2939. Prime factorization of 17634 in exponential form is:

17634 = 2¹ × 3¹ × 2939¹

Step-3: Factors of 17625

List of positive integer factors of 17625 that divides 17625 without a remainder.

1, 3, 5, 15, 25, 47, 75, 125, 141, 235, 375, 705, 1175, 3525, 5875

Step-4: Factors of 17634

List of positive integer factors of 17634 that divides 17625 without a remainder.

1, 2, 3, 6, 2939, 5878, 8817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17625 and 17634. The biggest common factor number is the GCF number.
So the greatest common factor 17625 and 17634 is 3.

Also check out the Least Common Multiple of 17625 and 17634