What is the Greatest Common Factor of 45984 and 46000?

Greatest common factor (GCF) of 45984 and 46000 is 16.

GCF(45984,46000) = 16

We will now calculate the prime factors of 45984 and 46000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45984 and 46000.

How to find the GCF of 45984 and 46000?

We will first find the prime factorization of 45984 and 46000. After we will calculate the factors of 45984 and 46000 and find the biggest common factor number .

Step-1: Prime Factorization of 45984

Prime factors of 45984 are 2, 3, 479. Prime factorization of 45984 in exponential form is:

45984 = 2⁵ × 3¹ × 479¹

Step-2: Prime Factorization of 46000

Prime factors of 46000 are 2, 5, 23. Prime factorization of 46000 in exponential form is:

46000 = 2⁴ × 5³ × 23¹

Step-3: Factors of 45984

List of positive integer factors of 45984 that divides 45984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 479, 958, 1437, 1916, 2874, 3832, 5748, 7664, 11496, 15328, 22992

Step-4: Factors of 46000

List of positive integer factors of 46000 that divides 45984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 25, 40, 46, 50, 80, 92, 100, 115, 125, 184, 200, 230, 250, 368, 400, 460, 500, 575, 920, 1000, 1150, 1840, 2000, 2300, 2875, 4600, 5750, 9200, 11500, 23000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45984 and 46000. The biggest common factor number is the GCF number.
So the greatest common factor 45984 and 46000 is 16.

Also check out the Least Common Multiple of 45984 and 46000