What is the Greatest Common Factor of 49600 and 49608?

Greatest common factor (GCF) of 49600 and 49608 is 8.

GCF(49600,49608) = 8

We will now calculate the prime factors of 49600 and 49608, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49600 and 49608.

How to find the GCF of 49600 and 49608?

We will first find the prime factorization of 49600 and 49608. After we will calculate the factors of 49600 and 49608 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 49608

Prime factors of 49608 are 2, 3, 13, 53. Prime factorization of 49608 in exponential form is:

49608 = 2³ × 3² × 13¹ × 53¹

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 49608

List of positive integer factors of 49608 that divides 49600 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 53, 72, 78, 104, 106, 117, 156, 159, 212, 234, 312, 318, 424, 468, 477, 636, 689, 936, 954, 1272, 1378, 1908, 2067, 2756, 3816, 4134, 5512, 6201, 8268, 12402, 16536, 24804

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49600 and 49608. The biggest common factor number is the GCF number.
So the greatest common factor 49600 and 49608 is 8.

Also check out the Least Common Multiple of 49600 and 49608