What is the Greatest Common Factor of 33969 and 33984?

Greatest common factor (GCF) of 33969 and 33984 is 3.

GCF(33969,33984) = 3

We will now calculate the prime factors of 33969 and 33984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33969 and 33984.

How to find the GCF of 33969 and 33984?

We will first find the prime factorization of 33969 and 33984. After we will calculate the factors of 33969 and 33984 and find the biggest common factor number .

Step-1: Prime Factorization of 33969

Prime factors of 33969 are 3, 13, 67. Prime factorization of 33969 in exponential form is:

33969 = 3¹ × 13² × 67¹

Step-2: Prime Factorization of 33984

Prime factors of 33984 are 2, 3, 59. Prime factorization of 33984 in exponential form is:

33984 = 2⁶ × 3² × 59¹

Step-3: Factors of 33969

List of positive integer factors of 33969 that divides 33969 without a remainder.

1, 3, 13, 39, 67, 169, 201, 507, 871, 2613, 11323

Step-4: Factors of 33984

List of positive integer factors of 33984 that divides 33969 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 59, 64, 72, 96, 118, 144, 177, 192, 236, 288, 354, 472, 531, 576, 708, 944, 1062, 1416, 1888, 2124, 2832, 3776, 4248, 5664, 8496, 11328, 16992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33969 and 33984. The biggest common factor number is the GCF number.
So the greatest common factor 33969 and 33984 is 3.

Also check out the Least Common Multiple of 33969 and 33984