What is the Greatest Common Factor of 49560 and 49575?

Greatest common factor (GCF) of 49560 and 49575 is 15.

GCF(49560,49575) = 15

We will now calculate the prime factors of 49560 and 49575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49560 and 49575.

How to find the GCF of 49560 and 49575?

We will first find the prime factorization of 49560 and 49575. After we will calculate the factors of 49560 and 49575 and find the biggest common factor number .

Step-1: Prime Factorization of 49560

Prime factors of 49560 are 2, 3, 5, 7, 59. Prime factorization of 49560 in exponential form is:

49560 = 2³ × 3¹ × 5¹ × 7¹ × 59¹

Step-2: Prime Factorization of 49575

Prime factors of 49575 are 3, 5, 661. Prime factorization of 49575 in exponential form is:

49575 = 3¹ × 5² × 661¹

Step-3: Factors of 49560

List of positive integer factors of 49560 that divides 49560 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 59, 60, 70, 84, 105, 118, 120, 140, 168, 177, 210, 236, 280, 295, 354, 413, 420, 472, 590, 708, 826, 840, 885, 1180, 1239, 1416, 1652, 1770, 2065, 2360, 2478, 3304, 3540, 4130, 4956, 6195, 7080, 8260, 9912, 12390, 16520, 24780

Step-4: Factors of 49575

List of positive integer factors of 49575 that divides 49560 without a remainder.

1, 3, 5, 15, 25, 75, 661, 1983, 3305, 9915, 16525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49560 and 49575. The biggest common factor number is the GCF number.
So the greatest common factor 49560 and 49575 is 15.

Also check out the Least Common Multiple of 49560 and 49575