What is the Greatest Common Factor of 33953 and 33972?

Greatest common factor (GCF) of 33953 and 33972 is 19.

GCF(33953,33972) = 19

We will now calculate the prime factors of 33953 and 33972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33953 and 33972.

How to find the GCF of 33953 and 33972?

We will first find the prime factorization of 33953 and 33972. After we will calculate the factors of 33953 and 33972 and find the biggest common factor number .

Step-1: Prime Factorization of 33953

Prime factors of 33953 are 19, 1787. Prime factorization of 33953 in exponential form is:

33953 = 19¹ × 1787¹

Step-2: 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-3: Factors of 33953

List of positive integer factors of 33953 that divides 33953 without a remainder.

1, 19, 1787

Step-4: Factors of 33972

List of positive integer factors of 33972 that divides 33953 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33953 and 33972. The biggest common factor number is the GCF number.
So the greatest common factor 33953 and 33972 is 19.

Also check out the Least Common Multiple of 33953 and 33972