What is the Greatest Common Factor of 42000 and 42010?

Greatest common factor (GCF) of 42000 and 42010 is 10.

GCF(42000,42010) = 10

We will now calculate the prime factors of 42000 and 42010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42000 and 42010.

How to find the GCF of 42000 and 42010?

We will first find the prime factorization of 42000 and 42010. After we will calculate the factors of 42000 and 42010 and find the biggest common factor number .

Step-1: Prime Factorization of 42000

Prime factors of 42000 are 2, 3, 5, 7. Prime factorization of 42000 in exponential form is:

42000 = 2⁴ × 3¹ × 5³ × 7¹

Step-2: Prime Factorization of 42010

Prime factors of 42010 are 2, 5, 4201. Prime factorization of 42010 in exponential form is:

42010 = 2¹ × 5¹ × 4201¹

Step-3: Factors of 42000

List of positive integer factors of 42000 that divides 42000 without a remainder.

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

Step-4: Factors of 42010

List of positive integer factors of 42010 that divides 42000 without a remainder.

1, 2, 5, 10, 4201, 8402, 21005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42000 and 42010. The biggest common factor number is the GCF number.
So the greatest common factor 42000 and 42010 is 10.

Also check out the Least Common Multiple of 42000 and 42010