What is the Greatest Common Factor of 33120 and 33138?

Greatest common factor (GCF) of 33120 and 33138 is 18.

GCF(33120,33138) = 18

We will now calculate the prime factors of 33120 and 33138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33120 and 33138.

How to find the GCF of 33120 and 33138?

We will first find the prime factorization of 33120 and 33138. After we will calculate the factors of 33120 and 33138 and find the biggest common factor number .

Step-1: Prime Factorization of 33120

Prime factors of 33120 are 2, 3, 5, 23. Prime factorization of 33120 in exponential form is:

33120 = 2⁵ × 3² × 5¹ × 23¹

Step-2: Prime Factorization of 33138

Prime factors of 33138 are 2, 3, 7, 263. Prime factorization of 33138 in exponential form is:

33138 = 2¹ × 3² × 7¹ × 263¹

Step-3: Factors of 33120

List of positive integer factors of 33120 that divides 33120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 30, 32, 36, 40, 45, 46, 48, 60, 69, 72, 80, 90, 92, 96, 115, 120, 138, 144, 160, 180, 184, 207, 230, 240, 276, 288, 345, 360, 368, 414, 460, 480, 552, 690, 720, 736, 828, 920, 1035, 1104, 1380, 1440, 1656, 1840, 2070, 2208, 2760, 3312, 3680, 4140, 5520, 6624, 8280, 11040, 16560

Step-4: Factors of 33138

List of positive integer factors of 33138 that divides 33120 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 263, 526, 789, 1578, 1841, 2367, 3682, 4734, 5523, 11046, 16569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33120 and 33138. The biggest common factor number is the GCF number.
So the greatest common factor 33120 and 33138 is 18.

Also check out the Least Common Multiple of 33120 and 33138