What is the Greatest Common Factor of 992 and 1008?

Greatest common factor (GCF) of 992 and 1008 is 16.

GCF(992,1008) = 16

We will now calculate the prime factors of 992 and 1008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 992 and 1008.

How to find the GCF of 992 and 1008?

We will first find the prime factorization of 992 and 1008. After we will calculate the factors of 992 and 1008 and find the biggest common factor number .

Step-1: Prime Factorization of 992

Prime factors of 992 are 2, 31. Prime factorization of 992 in exponential form is:

992 = 2⁵ × 31¹

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 992

List of positive integer factors of 992 that divides 992 without a remainder.

1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496

Step-4: Factors of 1008

List of positive integer factors of 1008 that divides 992 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 992 and 1008. The biggest common factor number is the GCF number.
So the greatest common factor 992 and 1008 is 16.

Also check out the Least Common Multiple of 992 and 1008