What is the Greatest Common Factor of 49600 and 49616?

Greatest common factor (GCF) of 49600 and 49616 is 16.

GCF(49600,49616) = 16

We will now calculate the prime factors of 49600 and 49616, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49600 and 49616.

How to find the GCF of 49600 and 49616?

We will first find the prime factorization of 49600 and 49616. After we will calculate the factors of 49600 and 49616 and find the biggest common factor number .

Step-1: Prime Factorization of 49600

Prime factors of 49600 are 2, 5, 31. Prime factorization of 49600 in exponential form is:

49600 = 2⁶ × 5² × 31¹

Step-2: Prime Factorization of 49616

Prime factors of 49616 are 2, 7, 443. Prime factorization of 49616 in exponential form is:

49616 = 2⁴ × 7¹ × 443¹

Step-3: Factors of 49600

List of positive integer factors of 49600 that divides 49600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 31, 32, 40, 50, 62, 64, 80, 100, 124, 155, 160, 200, 248, 310, 320, 400, 496, 620, 775, 800, 992, 1240, 1550, 1600, 1984, 2480, 3100, 4960, 6200, 9920, 12400, 24800

Step-4: Factors of 49616

List of positive integer factors of 49616 that divides 49600 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 443, 886, 1772, 3101, 3544, 6202, 7088, 12404, 24808

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49600 and 49616. The biggest common factor number is the GCF number.
So the greatest common factor 49600 and 49616 is 16.

Also check out the Least Common Multiple of 49600 and 49616