What is the Greatest Common Factor of 33600 and 33605?

Greatest common factor (GCF) of 33600 and 33605 is 5.

GCF(33600,33605) = 5

We will now calculate the prime factors of 33600 and 33605, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33600 and 33605.

How to find the GCF of 33600 and 33605?

We will first find the prime factorization of 33600 and 33605. After we will calculate the factors of 33600 and 33605 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 33605

Prime factors of 33605 are 5, 11, 13, 47. Prime factorization of 33605 in exponential form is:

33605 = 5¹ × 11¹ × 13¹ × 47¹

Step-3: Factors of 33600

List of positive integer factors of 33600 that divides 33600 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

Step-4: Factors of 33605

List of positive integer factors of 33605 that divides 33600 without a remainder.

1, 5, 11, 13, 47, 55, 65, 143, 235, 517, 611, 715, 2585, 3055, 6721

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33600 and 33605. The biggest common factor number is the GCF number.
So the greatest common factor 33600 and 33605 is 5.

Also check out the Least Common Multiple of 33600 and 33605