What is the Greatest Common Factor of 31980 and 32000?

Greatest common factor (GCF) of 31980 and 32000 is 20.

GCF(31980,32000) = 20

We will now calculate the prime factors of 31980 and 32000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31980 and 32000.

How to find the GCF of 31980 and 32000?

We will first find the prime factorization of 31980 and 32000. After we will calculate the factors of 31980 and 32000 and find the biggest common factor number .

Step-1: Prime Factorization of 31980

Prime factors of 31980 are 2, 3, 5, 13, 41. Prime factorization of 31980 in exponential form is:

31980 = 2² × 3¹ × 5¹ × 13¹ × 41¹

Step-2: Prime Factorization of 32000

Prime factors of 32000 are 2, 5. Prime factorization of 32000 in exponential form is:

32000 = 2⁸ × 5³

Step-3: Factors of 31980

List of positive integer factors of 31980 that divides 31980 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 41, 52, 60, 65, 78, 82, 123, 130, 156, 164, 195, 205, 246, 260, 390, 410, 492, 533, 615, 780, 820, 1066, 1230, 1599, 2132, 2460, 2665, 3198, 5330, 6396, 7995, 10660, 15990

Step-4: Factors of 32000

List of positive integer factors of 32000 that divides 31980 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 640, 800, 1000, 1280, 1600, 2000, 3200, 4000, 6400, 8000, 16000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31980 and 32000. The biggest common factor number is the GCF number.
So the greatest common factor 31980 and 32000 is 20.

Also check out the Least Common Multiple of 31980 and 32000