What is the Greatest Common Factor of 84000 and 84008?

Greatest common factor (GCF) of 84000 and 84008 is 8.

GCF(84000,84008) = 8

We will now calculate the prime factors of 84000 and 84008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84000 and 84008.

How to find the GCF of 84000 and 84008?

We will first find the prime factorization of 84000 and 84008. After we will calculate the factors of 84000 and 84008 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 84008

Prime factors of 84008 are 2, 10501. Prime factorization of 84008 in exponential form is:

84008 = 2³ × 10501¹

Step-3: Factors of 84000

List of positive integer factors of 84000 that divides 84000 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

Step-4: Factors of 84008

List of positive integer factors of 84008 that divides 84000 without a remainder.

1, 2, 4, 8, 10501, 21002, 42004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84000 and 84008. The biggest common factor number is the GCF number.
So the greatest common factor 84000 and 84008 is 8.

Also check out the Least Common Multiple of 84000 and 84008