What is the Greatest Common Factor of 75225 and 75240?

Greatest common factor (GCF) of 75225 and 75240 is 15.

GCF(75225,75240) = 15

We will now calculate the prime factors of 75225 and 75240, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75225 and 75240.

How to find the GCF of 75225 and 75240?

We will first find the prime factorization of 75225 and 75240. After we will calculate the factors of 75225 and 75240 and find the biggest common factor number .

Step-1: Prime Factorization of 75225

Prime factors of 75225 are 3, 5, 17, 59. Prime factorization of 75225 in exponential form is:

75225 = 3¹ × 5² × 17¹ × 59¹

Step-2: Prime Factorization of 75240

Prime factors of 75240 are 2, 3, 5, 11, 19. Prime factorization of 75240 in exponential form is:

75240 = 2³ × 3² × 5¹ × 11¹ × 19¹

Step-3: Factors of 75225

List of positive integer factors of 75225 that divides 75225 without a remainder.

1, 3, 5, 15, 17, 25, 51, 59, 75, 85, 177, 255, 295, 425, 885, 1003, 1275, 1475, 3009, 4425, 5015, 15045, 25075

Step-4: Factors of 75240

List of positive integer factors of 75240 that divides 75225 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 19, 20, 22, 24, 30, 33, 36, 38, 40, 44, 45, 55, 57, 60, 66, 72, 76, 88, 90, 95, 99, 110, 114, 120, 132, 152, 165, 171, 180, 190, 198, 209, 220, 228, 264, 285, 330, 342, 360, 380, 396, 418, 440, 456, 495, 570, 627, 660, 684, 760, 792, 836, 855, 990, 1045, 1140, 1254, 1320, 1368, 1672, 1710, 1881, 1980, 2090, 2280, 2508, 3135, 3420, 3762, 3960, 4180, 5016, 6270, 6840, 7524, 8360, 9405, 12540, 15048, 18810, 25080, 37620

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75225 and 75240. The biggest common factor number is the GCF number.
So the greatest common factor 75225 and 75240 is 15.

Also check out the Least Common Multiple of 75225 and 75240