What is the Greatest Common Factor of 33728 and 33740?

Greatest common factor (GCF) of 33728 and 33740 is 4.

GCF(33728,33740) = 4

We will now calculate the prime factors of 33728 and 33740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33728 and 33740.

How to find the GCF of 33728 and 33740?

We will first find the prime factorization of 33728 and 33740. After we will calculate the factors of 33728 and 33740 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 33740

Prime factors of 33740 are 2, 5, 7, 241. Prime factorization of 33740 in exponential form is:

33740 = 2² × 5¹ × 7¹ × 241¹

Step-3: Factors of 33728

List of positive integer factors of 33728 that divides 33728 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

Step-4: Factors of 33740

List of positive integer factors of 33740 that divides 33728 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 241, 482, 964, 1205, 1687, 2410, 3374, 4820, 6748, 8435, 16870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33728 and 33740. The biggest common factor number is the GCF number.
So the greatest common factor 33728 and 33740 is 4.

Also check out the Least Common Multiple of 33728 and 33740