What is the Greatest Common Factor of 49742 and 49760?

Greatest common factor (GCF) of 49742 and 49760 is 2.

GCF(49742,49760) = 2

We will now calculate the prime factors of 49742 and 49760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49742 and 49760.

How to find the GCF of 49742 and 49760?

We will first find the prime factorization of 49742 and 49760. After we will calculate the factors of 49742 and 49760 and find the biggest common factor number .

Step-1: Prime Factorization of 49742

Prime factors of 49742 are 2, 7, 11, 17, 19. Prime factorization of 49742 in exponential form is:

49742 = 2¹ × 7¹ × 11¹ × 17¹ × 19¹

Step-2: Prime Factorization of 49760

Prime factors of 49760 are 2, 5, 311. Prime factorization of 49760 in exponential form is:

49760 = 2⁵ × 5¹ × 311¹

Step-3: Factors of 49742

List of positive integer factors of 49742 that divides 49742 without a remainder.

1, 2, 7, 11, 14, 17, 19, 22, 34, 38, 77, 119, 133, 154, 187, 209, 238, 266, 323, 374, 418, 646, 1309, 1463, 2261, 2618, 2926, 3553, 4522, 7106, 24871

Step-4: Factors of 49760

List of positive integer factors of 49760 that divides 49742 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 311, 622, 1244, 1555, 2488, 3110, 4976, 6220, 9952, 12440, 24880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49742 and 49760. The biggest common factor number is the GCF number.
So the greatest common factor 49742 and 49760 is 2.

Also check out the Least Common Multiple of 49742 and 49760