What is the Greatest Common Factor of 41993 and 42000?

Greatest common factor (GCF) of 41993 and 42000 is 7.

GCF(41993,42000) = 7

We will now calculate the prime factors of 41993 and 42000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41993 and 42000.

How to find the GCF of 41993 and 42000?

We will first find the prime factorization of 41993 and 42000. After we will calculate the factors of 41993 and 42000 and find the biggest common factor number .

Step-1: Prime Factorization of 41993

Prime factors of 41993 are 7, 857. Prime factorization of 41993 in exponential form is:

41993 = 7² × 857¹

Step-2: 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-3: Factors of 41993

List of positive integer factors of 41993 that divides 41993 without a remainder.

1, 7, 49, 857, 5999

Step-4: Factors of 42000

List of positive integer factors of 42000 that divides 41993 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 41993 and 42000. The biggest common factor number is the GCF number.
So the greatest common factor 41993 and 42000 is 7.

Also check out the Least Common Multiple of 41993 and 42000