What is the Greatest Common Factor of 84000 and 84015?

Greatest common factor (GCF) of 84000 and 84015 is 15.

GCF(84000,84015) = 15

We will now calculate the prime factors of 84000 and 84015, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84000 and 84015.

How to find the GCF of 84000 and 84015?

We will first find the prime factorization of 84000 and 84015. After we will calculate the factors of 84000 and 84015 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 84015

Prime factors of 84015 are 3, 5, 1867. Prime factorization of 84015 in exponential form is:

84015 = 3² × 5¹ × 1867¹

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 84015

List of positive integer factors of 84015 that divides 84000 without a remainder.

1, 3, 5, 9, 15, 45, 1867, 5601, 9335, 16803, 28005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84000 and 84015. The biggest common factor number is the GCF number.
So the greatest common factor 84000 and 84015 is 15.

Also check out the Least Common Multiple of 84000 and 84015