What is the Greatest Common Factor of 17625 and 17640?

Greatest common factor (GCF) of 17625 and 17640 is 15.

GCF(17625,17640) = 15

We will now calculate the prime factors of 17625 and 17640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17625 and 17640.

How to find the GCF of 17625 and 17640?

We will first find the prime factorization of 17625 and 17640. After we will calculate the factors of 17625 and 17640 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 17640

Prime factors of 17640 are 2, 3, 5, 7. Prime factorization of 17640 in exponential form is:

17640 = 2³ × 3² × 5¹ × 7²

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 17640

List of positive integer factors of 17640 that divides 17625 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 49, 56, 60, 63, 70, 72, 84, 90, 98, 105, 120, 126, 140, 147, 168, 180, 196, 210, 245, 252, 280, 294, 315, 360, 392, 420, 441, 490, 504, 588, 630, 735, 840, 882, 980, 1176, 1260, 1470, 1764, 1960, 2205, 2520, 2940, 3528, 4410, 5880, 8820

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17625 and 17640. The biggest common factor number is the GCF number.
So the greatest common factor 17625 and 17640 is 15.

Also check out the Least Common Multiple of 17625 and 17640