What is the Greatest Common Factor of 32780 and 32800?

Greatest common factor (GCF) of 32780 and 32800 is 20.

GCF(32780,32800) = 20

We will now calculate the prime factors of 32780 and 32800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32780 and 32800.

How to find the GCF of 32780 and 32800?

We will first find the prime factorization of 32780 and 32800. After we will calculate the factors of 32780 and 32800 and find the biggest common factor number .

Step-1: Prime Factorization of 32780

Prime factors of 32780 are 2, 5, 11, 149. Prime factorization of 32780 in exponential form is:

32780 = 2² × 5¹ × 11¹ × 149¹

Step-2: Prime Factorization of 32800

Prime factors of 32800 are 2, 5, 41. Prime factorization of 32800 in exponential form is:

32800 = 2⁵ × 5² × 41¹

Step-3: Factors of 32780

List of positive integer factors of 32780 that divides 32780 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 149, 220, 298, 596, 745, 1490, 1639, 2980, 3278, 6556, 8195, 16390

Step-4: Factors of 32800

List of positive integer factors of 32800 that divides 32780 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 41, 50, 80, 82, 100, 160, 164, 200, 205, 328, 400, 410, 656, 800, 820, 1025, 1312, 1640, 2050, 3280, 4100, 6560, 8200, 16400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32780 and 32800. The biggest common factor number is the GCF number.
So the greatest common factor 32780 and 32800 is 20.

Also check out the Least Common Multiple of 32780 and 32800