What is the Greatest Common Factor of 33960 and 33972?

Greatest common factor (GCF) of 33960 and 33972 is 12.

GCF(33960,33972) = 12

We will now calculate the prime factors of 33960 and 33972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33960 and 33972.

How to find the GCF of 33960 and 33972?

We will first find the prime factorization of 33960 and 33972. After we will calculate the factors of 33960 and 33972 and find the biggest common factor number .

Step-1: Prime Factorization of 33960

Prime factors of 33960 are 2, 3, 5, 283. Prime factorization of 33960 in exponential form is:

33960 = 2³ × 3¹ × 5¹ × 283¹

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 33960

List of positive integer factors of 33960 that divides 33960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 283, 566, 849, 1132, 1415, 1698, 2264, 2830, 3396, 4245, 5660, 6792, 8490, 11320, 16980

Step-4: Factors of 33972

List of positive integer factors of 33972 that divides 33960 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 33960 and 33972. The biggest common factor number is the GCF number.
So the greatest common factor 33960 and 33972 is 12.

Also check out the Least Common Multiple of 33960 and 33972