What is the Greatest Common Factor of 33972 and 33991?

Greatest common factor (GCF) of 33972 and 33991 is 19.

GCF(33972,33991) = 19

We will now calculate the prime factors of 33972 and 33991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33972 and 33991.

How to find the GCF of 33972 and 33991?

We will first find the prime factorization of 33972 and 33991. After we will calculate the factors of 33972 and 33991 and find the biggest common factor number .

Step-1: Prime Factorization of 33972

Prime factors of 33972 are 2, 3, 19, 149. Prime factorization of 33972 in exponential form is:

33972 = 2² × 3¹ × 19¹ × 149¹

Step-2: Prime Factorization of 33991

Prime factors of 33991 are 19, 1789. Prime factorization of 33991 in exponential form is:

33991 = 19¹ × 1789¹

Step-3: Factors of 33972

List of positive integer factors of 33972 that divides 33972 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 149, 228, 298, 447, 596, 894, 1788, 2831, 5662, 8493, 11324, 16986

Step-4: Factors of 33991

List of positive integer factors of 33991 that divides 33972 without a remainder.

1, 19, 1789

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33972 and 33991. The biggest common factor number is the GCF number.
So the greatest common factor 33972 and 33991 is 19.

Also check out the Least Common Multiple of 33972 and 33991