What is the Greatest Common Factor of 33000 and 33005?

Greatest common factor (GCF) of 33000 and 33005 is 5.

GCF(33000,33005) = 5

We will now calculate the prime factors of 33000 and 33005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33000 and 33005.

How to find the GCF of 33000 and 33005?

We will first find the prime factorization of 33000 and 33005. After we will calculate the factors of 33000 and 33005 and find the biggest common factor number .

Step-1: Prime Factorization of 33000

Prime factors of 33000 are 2, 3, 5, 11. Prime factorization of 33000 in exponential form is:

33000 = 2³ × 3¹ × 5³ × 11¹

Step-2: Prime Factorization of 33005

Prime factors of 33005 are 5, 7, 23, 41. Prime factorization of 33005 in exponential form is:

33005 = 5¹ × 7¹ × 23¹ × 41¹

Step-3: Factors of 33000

List of positive integer factors of 33000 that divides 33000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 40, 44, 50, 55, 60, 66, 75, 88, 100, 110, 120, 125, 132, 150, 165, 200, 220, 250, 264, 275, 300, 330, 375, 440, 500, 550, 600, 660, 750, 825, 1000, 1100, 1320, 1375, 1500, 1650, 2200, 2750, 3000, 3300, 4125, 5500, 6600, 8250, 11000, 16500

Step-4: Factors of 33005

List of positive integer factors of 33005 that divides 33000 without a remainder.

1, 5, 7, 23, 35, 41, 115, 161, 205, 287, 805, 943, 1435, 4715, 6601

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33000 and 33005. The biggest common factor number is the GCF number.
So the greatest common factor 33000 and 33005 is 5.

Also check out the Least Common Multiple of 33000 and 33005