What is the Greatest Common Factor of 49708 and 49728?

Greatest common factor (GCF) of 49708 and 49728 is 4.

GCF(49708,49728) = 4

We will now calculate the prime factors of 49708 and 49728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49708 and 49728.

How to find the GCF of 49708 and 49728?

We will first find the prime factorization of 49708 and 49728. After we will calculate the factors of 49708 and 49728 and find the biggest common factor number .

Step-1: Prime Factorization of 49708

Prime factors of 49708 are 2, 17, 43. Prime factorization of 49708 in exponential form is:

49708 = 2² × 17² × 43¹

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 49708

List of positive integer factors of 49708 that divides 49708 without a remainder.

1, 2, 4, 17, 34, 43, 68, 86, 172, 289, 578, 731, 1156, 1462, 2924, 12427, 24854

Step-4: Factors of 49728

List of positive integer factors of 49728 that divides 49708 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 49708 and 49728. The biggest common factor number is the GCF number.
So the greatest common factor 49708 and 49728 is 4.

Also check out the Least Common Multiple of 49708 and 49728