What is the Greatest Common Factor of 33720 and 33728?

Greatest common factor (GCF) of 33720 and 33728 is 8.

GCF(33720,33728) = 8

We will now calculate the prime factors of 33720 and 33728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33720 and 33728.

How to find the GCF of 33720 and 33728?

We will first find the prime factorization of 33720 and 33728. After we will calculate the factors of 33720 and 33728 and find the biggest common factor number .

Step-1: Prime Factorization of 33720

Prime factors of 33720 are 2, 3, 5, 281. Prime factorization of 33720 in exponential form is:

33720 = 2³ × 3¹ × 5¹ × 281¹

Step-2: Prime Factorization of 33728

Prime factors of 33728 are 2, 17, 31. Prime factorization of 33728 in exponential form is:

33728 = 2⁶ × 17¹ × 31¹

Step-3: Factors of 33720

List of positive integer factors of 33720 that divides 33720 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 281, 562, 843, 1124, 1405, 1686, 2248, 2810, 3372, 4215, 5620, 6744, 8430, 11240, 16860

Step-4: Factors of 33728

List of positive integer factors of 33728 that divides 33720 without a remainder.

1, 2, 4, 8, 16, 17, 31, 32, 34, 62, 64, 68, 124, 136, 248, 272, 496, 527, 544, 992, 1054, 1088, 1984, 2108, 4216, 8432, 16864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33720 and 33728. The biggest common factor number is the GCF number.
So the greatest common factor 33720 and 33728 is 8.

Also check out the Least Common Multiple of 33720 and 33728