What is the Greatest Common Factor of 83993 and 84000?

Greatest common factor (GCF) of 83993 and 84000 is 7.

GCF(83993,84000) = 7

We will now calculate the prime factors of 83993 and 84000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83993 and 84000.

How to find the GCF of 83993 and 84000?

We will first find the prime factorization of 83993 and 84000. After we will calculate the factors of 83993 and 84000 and find the biggest common factor number .

Step-1: Prime Factorization of 83993

Prime factors of 83993 are 7, 13, 71. Prime factorization of 83993 in exponential form is:

83993 = 7¹ × 13² × 71¹

Step-2: Prime Factorization of 84000

Prime factors of 84000 are 2, 3, 5, 7. Prime factorization of 84000 in exponential form is:

84000 = 2⁵ × 3¹ × 5³ × 7¹

Step-3: Factors of 83993

List of positive integer factors of 83993 that divides 83993 without a remainder.

1, 7, 13, 71, 91, 169, 497, 923, 1183, 6461, 11999

Step-4: Factors of 84000

List of positive integer factors of 84000 that divides 83993 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 32, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 96, 100, 105, 112, 120, 125, 140, 150, 160, 168, 175, 200, 210, 224, 240, 250, 280, 300, 336, 350, 375, 400, 420, 480, 500, 525, 560, 600, 672, 700, 750, 800, 840, 875, 1000, 1050, 1120, 1200, 1400, 1500, 1680, 1750, 2000, 2100, 2400, 2625, 2800, 3000, 3360, 3500, 4000, 4200, 5250, 5600, 6000, 7000, 8400, 10500, 12000, 14000, 16800, 21000, 28000, 42000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83993 and 84000. The biggest common factor number is the GCF number.
So the greatest common factor 83993 and 84000 is 7.

Also check out the Least Common Multiple of 83993 and 84000