What is the Greatest Common Factor of 49728 and 49748?

Greatest common factor (GCF) of 49728 and 49748 is 4.

GCF(49728,49748) = 4

We will now calculate the prime factors of 49728 and 49748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49728 and 49748.

How to find the GCF of 49728 and 49748?

We will first find the prime factorization of 49728 and 49748. After we will calculate the factors of 49728 and 49748 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 49748

Prime factors of 49748 are 2, 12437. Prime factorization of 49748 in exponential form is:

49748 = 2² × 12437¹

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 49748

List of positive integer factors of 49748 that divides 49728 without a remainder.

1, 2, 4, 12437, 24874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49728 and 49748. The biggest common factor number is the GCF number.
So the greatest common factor 49728 and 49748 is 4.

Also check out the Least Common Multiple of 49728 and 49748