What is the Greatest Common Factor of 43984 and 44000?

Greatest common factor (GCF) of 43984 and 44000 is 16.

GCF(43984,44000) = 16

We will now calculate the prime factors of 43984 and 44000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 43984 and 44000.

How to find the GCF of 43984 and 44000?

We will first find the prime factorization of 43984 and 44000. After we will calculate the factors of 43984 and 44000 and find the biggest common factor number .

Step-1: Prime Factorization of 43984

Prime factors of 43984 are 2, 2749. Prime factorization of 43984 in exponential form is:

43984 = 2⁴ × 2749¹

Step-2: Prime Factorization of 44000

Prime factors of 44000 are 2, 5, 11. Prime factorization of 44000 in exponential form is:

44000 = 2⁵ × 5³ × 11¹

Step-3: Factors of 43984

List of positive integer factors of 43984 that divides 43984 without a remainder.

1, 2, 4, 8, 16, 2749, 5498, 10996, 21992

Step-4: Factors of 44000

List of positive integer factors of 44000 that divides 43984 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 80, 88, 100, 110, 125, 160, 176, 200, 220, 250, 275, 352, 400, 440, 500, 550, 800, 880, 1000, 1100, 1375, 1760, 2000, 2200, 2750, 4000, 4400, 5500, 8800, 11000, 22000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 43984 and 44000. The biggest common factor number is the GCF number.
So the greatest common factor 43984 and 44000 is 16.

Also check out the Least Common Multiple of 43984 and 44000