What is the Greatest Common Factor of 9225 and 9240?

Greatest common factor (GCF) of 9225 and 9240 is 15.

GCF(9225,9240) = 15

We will now calculate the prime factors of 9225 and 9240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9225 and 9240.

How to find the GCF of 9225 and 9240?

We will first find the prime factorization of 9225 and 9240. After we will calculate the factors of 9225 and 9240 and find the biggest common factor number .

Step-1: Prime Factorization of 9225

Prime factors of 9225 are 3, 5, 41. Prime factorization of 9225 in exponential form is:

9225 = 3² × 5² × 41¹

Step-2: Prime Factorization of 9240

Prime factors of 9240 are 2, 3, 5, 7, 11. Prime factorization of 9240 in exponential form is:

9240 = 2³ × 3¹ × 5¹ × 7¹ × 11¹

Step-3: Factors of 9225

List of positive integer factors of 9225 that divides 9225 without a remainder.

1, 3, 5, 9, 15, 25, 41, 45, 75, 123, 205, 225, 369, 615, 1025, 1845, 3075

Step-4: Factors of 9240

List of positive integer factors of 9240 that divides 9225 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22, 24, 28, 30, 33, 35, 40, 42, 44, 55, 56, 60, 66, 70, 77, 84, 88, 105, 110, 120, 132, 140, 154, 165, 168, 210, 220, 231, 264, 280, 308, 330, 385, 420, 440, 462, 616, 660, 770, 840, 924, 1155, 1320, 1540, 1848, 2310, 3080, 4620

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9225 and 9240. The biggest common factor number is the GCF number.
So the greatest common factor 9225 and 9240 is 15.

Also check out the Least Common Multiple of 9225 and 9240