What is the Greatest Common Factor of 32980 and 33000?

Greatest common factor (GCF) of 32980 and 33000 is 20.

GCF(32980,33000) = 20

We will now calculate the prime factors of 32980 and 33000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32980 and 33000.

How to find the GCF of 32980 and 33000?

We will first find the prime factorization of 32980 and 33000. After we will calculate the factors of 32980 and 33000 and find the biggest common factor number .

Step-1: Prime Factorization of 32980

Prime factors of 32980 are 2, 5, 17, 97. Prime factorization of 32980 in exponential form is:

32980 = 2² × 5¹ × 17¹ × 97¹

Step-2: 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-3: Factors of 32980

List of positive integer factors of 32980 that divides 32980 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 97, 170, 194, 340, 388, 485, 970, 1649, 1940, 3298, 6596, 8245, 16490

Step-4: Factors of 33000

List of positive integer factors of 33000 that divides 32980 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32980 and 33000. The biggest common factor number is the GCF number.
So the greatest common factor 32980 and 33000 is 20.

Also check out the Least Common Multiple of 32980 and 33000