What is the Greatest Common Factor of 32880 and 32900?

Greatest common factor (GCF) of 32880 and 32900 is 20.

GCF(32880,32900) = 20

We will now calculate the prime factors of 32880 and 32900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32880 and 32900.

How to find the GCF of 32880 and 32900?

We will first find the prime factorization of 32880 and 32900. After we will calculate the factors of 32880 and 32900 and find the biggest common factor number .

Step-1: Prime Factorization of 32880

Prime factors of 32880 are 2, 3, 5, 137. Prime factorization of 32880 in exponential form is:

32880 = 2⁴ × 3¹ × 5¹ × 137¹

Step-2: Prime Factorization of 32900

Prime factors of 32900 are 2, 5, 7, 47. Prime factorization of 32900 in exponential form is:

32900 = 2² × 5² × 7¹ × 47¹

Step-3: Factors of 32880

List of positive integer factors of 32880 that divides 32880 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 137, 240, 274, 411, 548, 685, 822, 1096, 1370, 1644, 2055, 2192, 2740, 3288, 4110, 5480, 6576, 8220, 10960, 16440

Step-4: Factors of 32900

List of positive integer factors of 32900 that divides 32880 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 47, 50, 70, 94, 100, 140, 175, 188, 235, 329, 350, 470, 658, 700, 940, 1175, 1316, 1645, 2350, 3290, 4700, 6580, 8225, 16450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32880 and 32900. The biggest common factor number is the GCF number.
So the greatest common factor 32880 and 32900 is 20.

Also check out the Least Common Multiple of 32880 and 32900