What is the Greatest Common Factor of 17625 and 17632?

Greatest common factor (GCF) of 17625 and 17632 is 1.

GCF(17625,17632) = 1

We will now calculate the prime factors of 17625 and 17632, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17625 and 17632.

How to find the GCF of 17625 and 17632?

We will first find the prime factorization of 17625 and 17632. After we will calculate the factors of 17625 and 17632 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 17632

Prime factors of 17632 are 2, 19, 29. Prime factorization of 17632 in exponential form is:

17632 = 2⁵ × 19¹ × 29¹

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 17632

List of positive integer factors of 17632 that divides 17625 without a remainder.

1, 2, 4, 8, 16, 19, 29, 32, 38, 58, 76, 116, 152, 232, 304, 464, 551, 608, 928, 1102, 2204, 4408, 8816

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17625 and 17632. The biggest common factor number is the GCF number.
So the greatest common factor 17625 and 17632 is 1.

Also check out the Least Common Multiple of 17625 and 17632