What is the Greatest Common Factor of 49728 and 49744?

Greatest common factor (GCF) of 49728 and 49744 is 16.

GCF(49728,49744) = 16

We will now calculate the prime factors of 49728 and 49744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49728 and 49744.

How to find the GCF of 49728 and 49744?

We will first find the prime factorization of 49728 and 49744. After we will calculate the factors of 49728 and 49744 and find the biggest common factor number .

Step-1: Prime Factorization of 49728

Prime factors of 49728 are 2, 3, 7, 37. Prime factorization of 49728 in exponential form is:

49728 = 2⁶ × 3¹ × 7¹ × 37¹

Step-2: Prime Factorization of 49744

Prime factors of 49744 are 2, 3109. Prime factorization of 49744 in exponential form is:

49744 = 2⁴ × 3109¹

Step-3: Factors of 49728

List of positive integer factors of 49728 that divides 49728 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 37, 42, 48, 56, 64, 74, 84, 96, 111, 112, 148, 168, 192, 222, 224, 259, 296, 336, 444, 448, 518, 592, 672, 777, 888, 1036, 1184, 1344, 1554, 1776, 2072, 2368, 3108, 3552, 4144, 6216, 7104, 8288, 12432, 16576, 24864

Step-4: Factors of 49744

List of positive integer factors of 49744 that divides 49728 without a remainder.

1, 2, 4, 8, 16, 3109, 6218, 12436, 24872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49728 and 49744. The biggest common factor number is the GCF number.
So the greatest common factor 49728 and 49744 is 16.

Also check out the Least Common Multiple of 49728 and 49744