What is the Greatest Common Factor of 41984 and 42000?

Greatest common factor (GCF) of 41984 and 42000 is 16.

GCF(41984,42000) = 16

We will now calculate the prime factors of 41984 and 42000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41984 and 42000.

How to find the GCF of 41984 and 42000?

We will first find the prime factorization of 41984 and 42000. After we will calculate the factors of 41984 and 42000 and find the biggest common factor number .

Step-1: Prime Factorization of 41984

Prime factors of 41984 are 2, 41. Prime factorization of 41984 in exponential form is:

41984 = 2¹⁰ × 41¹

Step-2: Prime Factorization of 42000

Prime factors of 42000 are 2, 3, 5, 7. Prime factorization of 42000 in exponential form is:

42000 = 2⁴ × 3¹ × 5³ × 7¹

Step-3: Factors of 41984

List of positive integer factors of 41984 that divides 41984 without a remainder.

1, 2, 4, 8, 16, 32, 41, 64, 82, 128, 164, 256, 328, 512, 656, 1024, 1312, 2624, 5248, 10496, 20992

Step-4: Factors of 42000

List of positive integer factors of 42000 that divides 41984 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 700, 750, 840, 875, 1000, 1050, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2625, 2800, 3000, 3500, 4200, 5250, 6000, 7000, 8400, 10500, 14000, 21000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 41984 and 42000. The biggest common factor number is the GCF number.
So the greatest common factor 41984 and 42000 is 16.

Also check out the Least Common Multiple of 41984 and 42000