What is the Greatest Common Factor of 84000 and 84019?

Greatest common factor (GCF) of 84000 and 84019 is 1.

GCF(84000,84019) = 1

We will now calculate the prime factors of 84000 and 84019, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84000 and 84019.

How to find the GCF of 84000 and 84019?

We will first find the prime factorization of 84000 and 84019. After we will calculate the factors of 84000 and 84019 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 84019

Prime factors of 84019 are 13, 23, 281. Prime factorization of 84019 in exponential form is:

84019 = 13¹ × 23¹ × 281¹

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 84019

List of positive integer factors of 84019 that divides 84000 without a remainder.

1, 13, 23, 281, 299, 3653, 6463

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84000 and 84019. The biggest common factor number is the GCF number.
So the greatest common factor 84000 and 84019 is 1.

Also check out the Least Common Multiple of 84000 and 84019