What is the Greatest Common Factor of 49724 and 49728?

Greatest common factor (GCF) of 49724 and 49728 is 4.

GCF(49724,49728) = 4

We will now calculate the prime factors of 49724 and 49728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49724 and 49728.

How to find the GCF of 49724 and 49728?

We will first find the prime factorization of 49724 and 49728. After we will calculate the factors of 49724 and 49728 and find the biggest common factor number .

Step-1: Prime Factorization of 49724

Prime factors of 49724 are 2, 31, 401. Prime factorization of 49724 in exponential form is:

49724 = 2² × 31¹ × 401¹

Step-2: 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-3: Factors of 49724

List of positive integer factors of 49724 that divides 49724 without a remainder.

1, 2, 4, 31, 62, 124, 401, 802, 1604, 12431, 24862

Step-4: Factors of 49728

List of positive integer factors of 49728 that divides 49724 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49724 and 49728. The biggest common factor number is the GCF number.
So the greatest common factor 49724 and 49728 is 4.

Also check out the Least Common Multiple of 49724 and 49728