What is the Greatest Common Factor of 1000 and 1008?

Greatest common factor (GCF) of 1000 and 1008 is 8.

GCF(1000,1008) = 8

We will now calculate the prime factors of 1000 and 1008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1000 and 1008.

How to find the GCF of 1000 and 1008?

We will first find the prime factorization of 1000 and 1008. After we will calculate the factors of 1000 and 1008 and find the biggest common factor number .

Step-1: Prime Factorization of 1000

Prime factors of 1000 are 2, 5. Prime factorization of 1000 in exponential form is:

1000 = 2³ × 5³

Step-2: Prime Factorization of 1008

Prime factors of 1008 are 2, 3, 7. Prime factorization of 1008 in exponential form is:

1008 = 2⁴ × 3² × 7¹

Step-3: Factors of 1000

List of positive integer factors of 1000 that divides 1000 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500

Step-4: Factors of 1008

List of positive integer factors of 1008 that divides 1000 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1000 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 1000 and 1008 is 8.

Also check out the Least Common Multiple of 1000 and 1008