What is the Greatest Common Factor of 75240 and 75259?

Greatest common factor (GCF) of 75240 and 75259 is 19.

GCF(75240,75259) = 19

We will now calculate the prime factors of 75240 and 75259, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75240 and 75259.

How to find the GCF of 75240 and 75259?

We will first find the prime factorization of 75240 and 75259. After we will calculate the factors of 75240 and 75259 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75259

Prime factors of 75259 are 17, 19, 233. Prime factorization of 75259 in exponential form is:

75259 = 17¹ × 19¹ × 233¹

Step-3: Factors of 75240

List of positive integer factors of 75240 that divides 75240 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

Step-4: Factors of 75259

List of positive integer factors of 75259 that divides 75240 without a remainder.

1, 17, 19, 233, 323, 3961, 4427

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75240 and 75259. The biggest common factor number is the GCF number.
So the greatest common factor 75240 and 75259 is 19.

Also check out the Least Common Multiple of 75240 and 75259