What is the Greatest Common Factor of 84000 and 84010?

Greatest common factor (GCF) of 84000 and 84010 is 10.

GCF(84000,84010) = 10

We will now calculate the prime factors of 84000 and 84010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84000 and 84010.

How to find the GCF of 84000 and 84010?

We will first find the prime factorization of 84000 and 84010. After we will calculate the factors of 84000 and 84010 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 84010

Prime factors of 84010 are 2, 5, 31, 271. Prime factorization of 84010 in exponential form is:

84010 = 2¹ × 5¹ × 31¹ × 271¹

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 84010

List of positive integer factors of 84010 that divides 84000 without a remainder.

1, 2, 5, 10, 31, 62, 155, 271, 310, 542, 1355, 2710, 8401, 16802, 42005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84000 and 84010. The biggest common factor number is the GCF number.
So the greatest common factor 84000 and 84010 is 10.

Also check out the Least Common Multiple of 84000 and 84010