What is the Greatest Common Factor of 33949 and 33966?

Greatest common factor (GCF) of 33949 and 33966 is 17.

GCF(33949,33966) = 17

We will now calculate the prime factors of 33949 and 33966, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33949 and 33966.

How to find the GCF of 33949 and 33966?

We will first find the prime factorization of 33949 and 33966. After we will calculate the factors of 33949 and 33966 and find the biggest common factor number .

Step-1: Prime Factorization of 33949

Prime factors of 33949 are 17, 1997. Prime factorization of 33949 in exponential form is:

33949 = 17¹ × 1997¹

Step-2: 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-3: Factors of 33949

List of positive integer factors of 33949 that divides 33949 without a remainder.

1, 17, 1997

Step-4: Factors of 33966

List of positive integer factors of 33966 that divides 33949 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33949 and 33966. The biggest common factor number is the GCF number.
So the greatest common factor 33949 and 33966 is 17.

Also check out the Least Common Multiple of 33949 and 33966