What is the Greatest Common Factor of 33966 and 33974?

Greatest common factor (GCF) of 33966 and 33974 is 2.

GCF(33966,33974) = 2

We will now calculate the prime factors of 33966 and 33974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33966 and 33974.

How to find the GCF of 33966 and 33974?

We will first find the prime factorization of 33966 and 33974. After we will calculate the factors of 33966 and 33974 and find the biggest common factor number .

Step-1: Prime Factorization of 33966

Prime factors of 33966 are 2, 3, 17, 37. Prime factorization of 33966 in exponential form is:

33966 = 2¹ × 3³ × 17¹ × 37¹

Step-2: Prime Factorization of 33974

Prime factors of 33974 are 2, 16987. Prime factorization of 33974 in exponential form is:

33974 = 2¹ × 16987¹

Step-3: Factors of 33966

List of positive integer factors of 33966 that divides 33966 without a remainder.

1, 2, 3, 6, 9, 17, 18, 27, 34, 37, 51, 54, 74, 102, 111, 153, 222, 306, 333, 459, 629, 666, 918, 999, 1258, 1887, 1998, 3774, 5661, 11322, 16983

Step-4: Factors of 33974

List of positive integer factors of 33974 that divides 33966 without a remainder.

1, 2, 16987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33966 and 33974. The biggest common factor number is the GCF number.
So the greatest common factor 33966 and 33974 is 2.

Also check out the Least Common Multiple of 33966 and 33974