What is the Greatest Common Factor of 33582 and 33600?

Greatest common factor (GCF) of 33582 and 33600 is 6.

GCF(33582,33600) = 6

We will now calculate the prime factors of 33582 and 33600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33582 and 33600.

How to find the GCF of 33582 and 33600?

We will first find the prime factorization of 33582 and 33600. After we will calculate the factors of 33582 and 33600 and find the biggest common factor number .

Step-1: Prime Factorization of 33582

Prime factors of 33582 are 2, 3, 29, 193. Prime factorization of 33582 in exponential form is:

33582 = 2¹ × 3¹ × 29¹ × 193¹

Step-2: Prime Factorization of 33600

Prime factors of 33600 are 2, 3, 5, 7. Prime factorization of 33600 in exponential form is:

33600 = 2⁶ × 3¹ × 5² × 7¹

Step-3: Factors of 33582

List of positive integer factors of 33582 that divides 33582 without a remainder.

1, 2, 3, 6, 29, 58, 87, 174, 193, 386, 579, 1158, 5597, 11194, 16791

Step-4: Factors of 33600

List of positive integer factors of 33600 that divides 33582 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 64, 70, 75, 80, 84, 96, 100, 105, 112, 120, 140, 150, 160, 168, 175, 192, 200, 210, 224, 240, 280, 300, 320, 336, 350, 400, 420, 448, 480, 525, 560, 600, 672, 700, 800, 840, 960, 1050, 1120, 1200, 1344, 1400, 1600, 1680, 2100, 2240, 2400, 2800, 3360, 4200, 4800, 5600, 6720, 8400, 11200, 16800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33582 and 33600. The biggest common factor number is the GCF number.
So the greatest common factor 33582 and 33600 is 6.

Also check out the Least Common Multiple of 33582 and 33600