What is the Greatest Common Factor of 33744 and 33760?

Greatest common factor (GCF) of 33744 and 33760 is 16.

GCF(33744,33760) = 16

We will now calculate the prime factors of 33744 and 33760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33744 and 33760.

How to find the GCF of 33744 and 33760?

We will first find the prime factorization of 33744 and 33760. After we will calculate the factors of 33744 and 33760 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 33760

Prime factors of 33760 are 2, 5, 211. Prime factorization of 33760 in exponential form is:

33760 = 2⁵ × 5¹ × 211¹

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 33760

List of positive integer factors of 33760 that divides 33744 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 211, 422, 844, 1055, 1688, 2110, 3376, 4220, 6752, 8440, 16880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33744 and 33760. The biggest common factor number is the GCF number.
So the greatest common factor 33744 and 33760 is 16.

Also check out the Least Common Multiple of 33744 and 33760