What is the Greatest Common Factor of 33729 and 33744?

Greatest common factor (GCF) of 33729 and 33744 is 3.

GCF(33729,33744) = 3

We will now calculate the prime factors of 33729 and 33744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33729 and 33744.

How to find the GCF of 33729 and 33744?

We will first find the prime factorization of 33729 and 33744. After we will calculate the factors of 33729 and 33744 and find the biggest common factor number .

Step-1: Prime Factorization of 33729

Prime factors of 33729 are 3, 11243. Prime factorization of 33729 in exponential form is:

33729 = 3¹ × 11243¹

Step-2: Prime Factorization of 33744

Prime factors of 33744 are 2, 3, 19, 37. Prime factorization of 33744 in exponential form is:

33744 = 2⁴ × 3¹ × 19¹ × 37¹

Step-3: Factors of 33729

List of positive integer factors of 33729 that divides 33729 without a remainder.

1, 3, 11243

Step-4: Factors of 33744

List of positive integer factors of 33744 that divides 33729 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 37, 38, 48, 57, 74, 76, 111, 114, 148, 152, 222, 228, 296, 304, 444, 456, 592, 703, 888, 912, 1406, 1776, 2109, 2812, 4218, 5624, 8436, 11248, 16872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33729 and 33744. The biggest common factor number is the GCF number.
So the greatest common factor 33729 and 33744 is 3.

Also check out the Least Common Multiple of 33729 and 33744