What is the Greatest Common Factor of 77984 and 78000?

Greatest common factor (GCF) of 77984 and 78000 is 16.

GCF(77984,78000) = 16

We will now calculate the prime factors of 77984 and 78000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77984 and 78000.

How to find the GCF of 77984 and 78000?

We will first find the prime factorization of 77984 and 78000. After we will calculate the factors of 77984 and 78000 and find the biggest common factor number .

Step-1: Prime Factorization of 77984

Prime factors of 77984 are 2, 2437. Prime factorization of 77984 in exponential form is:

77984 = 2⁵ × 2437¹

Step-2: Prime Factorization of 78000

Prime factors of 78000 are 2, 3, 5, 13. Prime factorization of 78000 in exponential form is:

78000 = 2⁴ × 3¹ × 5³ × 13¹

Step-3: Factors of 77984

List of positive integer factors of 77984 that divides 77984 without a remainder.

1, 2, 4, 8, 16, 32, 2437, 4874, 9748, 19496, 38992

Step-4: Factors of 78000

List of positive integer factors of 78000 that divides 77984 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 100, 104, 120, 125, 130, 150, 156, 195, 200, 208, 240, 250, 260, 300, 312, 325, 375, 390, 400, 500, 520, 600, 624, 650, 750, 780, 975, 1000, 1040, 1200, 1300, 1500, 1560, 1625, 1950, 2000, 2600, 3000, 3120, 3250, 3900, 4875, 5200, 6000, 6500, 7800, 9750, 13000, 15600, 19500, 26000, 39000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77984 and 78000. The biggest common factor number is the GCF number.
So the greatest common factor 77984 and 78000 is 16.

Also check out the Least Common Multiple of 77984 and 78000