What is the Greatest Common Factor of 61728 and 61744?

Greatest common factor (GCF) of 61728 and 61744 is 16.

GCF(61728,61744) = 16

We will now calculate the prime factors of 61728 and 61744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61728 and 61744.

How to find the GCF of 61728 and 61744?

We will first find the prime factorization of 61728 and 61744. After we will calculate the factors of 61728 and 61744 and find the biggest common factor number .

Step-1: Prime Factorization of 61728

Prime factors of 61728 are 2, 3, 643. Prime factorization of 61728 in exponential form is:

61728 = 2⁵ × 3¹ × 643¹

Step-2: Prime Factorization of 61744

Prime factors of 61744 are 2, 17, 227. Prime factorization of 61744 in exponential form is:

61744 = 2⁴ × 17¹ × 227¹

Step-3: Factors of 61728

List of positive integer factors of 61728 that divides 61728 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 643, 1286, 1929, 2572, 3858, 5144, 7716, 10288, 15432, 20576, 30864

Step-4: Factors of 61744

List of positive integer factors of 61744 that divides 61728 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 227, 272, 454, 908, 1816, 3632, 3859, 7718, 15436, 30872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61728 and 61744. The biggest common factor number is the GCF number.
So the greatest common factor 61728 and 61744 is 16.

Also check out the Least Common Multiple of 61728 and 61744