What is the Greatest Common Factor of 32480 and 32500?

Greatest common factor (GCF) of 32480 and 32500 is 20.

GCF(32480,32500) = 20

We will now calculate the prime factors of 32480 and 32500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32480 and 32500.

How to find the GCF of 32480 and 32500?

We will first find the prime factorization of 32480 and 32500. After we will calculate the factors of 32480 and 32500 and find the biggest common factor number .

Step-1: Prime Factorization of 32480

Prime factors of 32480 are 2, 5, 7, 29. Prime factorization of 32480 in exponential form is:

32480 = 2⁵ × 5¹ × 7¹ × 29¹

Step-2: Prime Factorization of 32500

Prime factors of 32500 are 2, 5, 13. Prime factorization of 32500 in exponential form is:

32500 = 2² × 5⁴ × 13¹

Step-3: Factors of 32480

List of positive integer factors of 32480 that divides 32480 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 29, 32, 35, 40, 56, 58, 70, 80, 112, 116, 140, 145, 160, 203, 224, 232, 280, 290, 406, 464, 560, 580, 812, 928, 1015, 1120, 1160, 1624, 2030, 2320, 3248, 4060, 4640, 6496, 8120, 16240

Step-4: Factors of 32500

List of positive integer factors of 32500 that divides 32480 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 125, 130, 250, 260, 325, 500, 625, 650, 1250, 1300, 1625, 2500, 3250, 6500, 8125, 16250

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32480 and 32500. The biggest common factor number is the GCF number.
So the greatest common factor 32480 and 32500 is 20.

Also check out the Least Common Multiple of 32480 and 32500