What is the Greatest Common Factor of 33960 and 33980?

Greatest common factor (GCF) of 33960 and 33980 is 20.

GCF(33960,33980) = 20

We will now calculate the prime factors of 33960 and 33980, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33960 and 33980.

How to find the GCF of 33960 and 33980?

We will first find the prime factorization of 33960 and 33980. After we will calculate the factors of 33960 and 33980 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 33980

Prime factors of 33980 are 2, 5, 1699. Prime factorization of 33980 in exponential form is:

33980 = 2² × 5¹ × 1699¹

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 33980

List of positive integer factors of 33980 that divides 33960 without a remainder.

1, 2, 4, 5, 10, 20, 1699, 3398, 6796, 8495, 16990

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33960 and 33980. The biggest common factor number is the GCF number.
So the greatest common factor 33960 and 33980 is 20.

Also check out the Least Common Multiple of 33960 and 33980