What is the Greatest Common Factor of 42000 and 42007?

Greatest common factor (GCF) of 42000 and 42007 is 7.

GCF(42000,42007) = 7

We will now calculate the prime factors of 42000 and 42007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42000 and 42007.

How to find the GCF of 42000 and 42007?

We will first find the prime factorization of 42000 and 42007. After we will calculate the factors of 42000 and 42007 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 42007

Prime factors of 42007 are 7, 17, 353. Prime factorization of 42007 in exponential form is:

42007 = 7¹ × 17¹ × 353¹

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 42007

List of positive integer factors of 42007 that divides 42000 without a remainder.

1, 7, 17, 119, 353, 2471, 6001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 42000 and 42007. The biggest common factor number is the GCF number.
So the greatest common factor 42000 and 42007 is 7.

Also check out the Least Common Multiple of 42000 and 42007