What is the Greatest Common Factor of 49584 and 49600?

Greatest common factor (GCF) of 49584 and 49600 is 16.

GCF(49584,49600) = 16

We will now calculate the prime factors of 49584 and 49600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49584 and 49600.

How to find the GCF of 49584 and 49600?

We will first find the prime factorization of 49584 and 49600. After we will calculate the factors of 49584 and 49600 and find the biggest common factor number .

Step-1: Prime Factorization of 49584

Prime factors of 49584 are 2, 3, 1033. Prime factorization of 49584 in exponential form is:

49584 = 2⁴ × 3¹ × 1033¹

Step-2: 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-3: Factors of 49584

List of positive integer factors of 49584 that divides 49584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1033, 2066, 3099, 4132, 6198, 8264, 12396, 16528, 24792

Step-4: Factors of 49600

List of positive integer factors of 49600 that divides 49584 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49584 and 49600. The biggest common factor number is the GCF number.
So the greatest common factor 49584 and 49600 is 16.

Also check out the Least Common Multiple of 49584 and 49600