What is the Greatest Common Factor of 17400 and 17415?

Greatest common factor (GCF) of 17400 and 17415 is 15.

GCF(17400,17415) = 15

We will now calculate the prime factors of 17400 and 17415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17400 and 17415.

How to find the GCF of 17400 and 17415?

We will first find the prime factorization of 17400 and 17415. After we will calculate the factors of 17400 and 17415 and find the biggest common factor number .

Step-1: Prime Factorization of 17400

Prime factors of 17400 are 2, 3, 5, 29. Prime factorization of 17400 in exponential form is:

17400 = 2³ × 3¹ × 5² × 29¹

Step-2: Prime Factorization of 17415

Prime factors of 17415 are 3, 5, 43. Prime factorization of 17415 in exponential form is:

17415 = 3⁴ × 5¹ × 43¹

Step-3: Factors of 17400

List of positive integer factors of 17400 that divides 17400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 29, 30, 40, 50, 58, 60, 75, 87, 100, 116, 120, 145, 150, 174, 200, 232, 290, 300, 348, 435, 580, 600, 696, 725, 870, 1160, 1450, 1740, 2175, 2900, 3480, 4350, 5800, 8700

Step-4: Factors of 17415

List of positive integer factors of 17415 that divides 17400 without a remainder.

1, 3, 5, 9, 15, 27, 43, 45, 81, 129, 135, 215, 387, 405, 645, 1161, 1935, 3483, 5805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17400 and 17415. The biggest common factor number is the GCF number.
So the greatest common factor 17400 and 17415 is 15.

Also check out the Least Common Multiple of 17400 and 17415