What is the Greatest Common Factor of 49560 and 49574?

Greatest common factor (GCF) of 49560 and 49574 is 14.

GCF(49560,49574) = 14

We will now calculate the prime factors of 49560 and 49574, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49560 and 49574.

How to find the GCF of 49560 and 49574?

We will first find the prime factorization of 49560 and 49574. After we will calculate the factors of 49560 and 49574 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 49574

Prime factors of 49574 are 2, 7, 3541. Prime factorization of 49574 in exponential form is:

49574 = 2¹ × 7¹ × 3541¹

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 49574

List of positive integer factors of 49574 that divides 49560 without a remainder.

1, 2, 7, 14, 3541, 7082, 24787

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49560 and 49574. The biggest common factor number is the GCF number.
So the greatest common factor 49560 and 49574 is 14.

Also check out the Least Common Multiple of 49560 and 49574