What is the Greatest Common Factor of 994 and 1008?

Greatest common factor (GCF) of 994 and 1008 is 14.

GCF(994,1008) = 14

We will now calculate the prime factors of 994 and 1008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 994 and 1008.

How to find the GCF of 994 and 1008?

We will first find the prime factorization of 994 and 1008. After we will calculate the factors of 994 and 1008 and find the biggest common factor number .

Step-1: Prime Factorization of 994

Prime factors of 994 are 2, 7, 71. Prime factorization of 994 in exponential form is:

994 = 2¹ × 7¹ × 71¹

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 994

List of positive integer factors of 994 that divides 994 without a remainder.

1, 2, 7, 14, 71, 142, 497

Step-4: Factors of 1008

List of positive integer factors of 1008 that divides 994 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 994 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 994 and 1008 is 14.

Also check out the Least Common Multiple of 994 and 1008