What is the Greatest Common Factor of 98400 and 98415?

Greatest common factor (GCF) of 98400 and 98415 is 15.

GCF(98400,98415) = 15

We will now calculate the prime factors of 98400 and 98415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 98400 and 98415.

How to find the GCF of 98400 and 98415?

We will first find the prime factorization of 98400 and 98415. After we will calculate the factors of 98400 and 98415 and find the biggest common factor number .

Step-1: Prime Factorization of 98400

Prime factors of 98400 are 2, 3, 5, 41. Prime factorization of 98400 in exponential form is:

98400 = 2⁵ × 3¹ × 5² × 41¹

Step-2: Prime Factorization of 98415

Prime factors of 98415 are 3, 5. Prime factorization of 98415 in exponential form is:

98415 = 3⁹ × 5¹

Step-3: Factors of 98400

List of positive integer factors of 98400 that divides 98400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 41, 48, 50, 60, 75, 80, 82, 96, 100, 120, 123, 150, 160, 164, 200, 205, 240, 246, 300, 328, 400, 410, 480, 492, 600, 615, 656, 800, 820, 984, 1025, 1200, 1230, 1312, 1640, 1968, 2050, 2400, 2460, 3075, 3280, 3936, 4100, 4920, 6150, 6560, 8200, 9840, 12300, 16400, 19680, 24600, 32800, 49200

Step-4: Factors of 98415

List of positive integer factors of 98415 that divides 98400 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 729, 1215, 2187, 3645, 6561, 10935, 19683, 32805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 98400 and 98415. The biggest common factor number is the GCF number.
So the greatest common factor 98400 and 98415 is 15.

Also check out the Least Common Multiple of 98400 and 98415