What is the Greatest Common Factor of 33744 and 33754?

Greatest common factor (GCF) of 33744 and 33754 is 2.

GCF(33744,33754) = 2

We will now calculate the prime factors of 33744 and 33754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33744 and 33754.

How to find the GCF of 33744 and 33754?

We will first find the prime factorization of 33744 and 33754. After we will calculate the factors of 33744 and 33754 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 33754

Prime factors of 33754 are 2, 7, 2411. Prime factorization of 33754 in exponential form is:

33754 = 2¹ × 7¹ × 2411¹

Step-3: Factors of 33744

List of positive integer factors of 33744 that divides 33744 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

Step-4: Factors of 33754

List of positive integer factors of 33754 that divides 33744 without a remainder.

1, 2, 7, 14, 2411, 4822, 16877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33744 and 33754. The biggest common factor number is the GCF number.
So the greatest common factor 33744 and 33754 is 2.

Also check out the Least Common Multiple of 33744 and 33754