What is the Greatest Common Factor of 2116 and 2128?

Greatest common factor (GCF) of 2116 and 2128 is 4.

GCF(2116,2128) = 4

We will now calculate the prime factors of 2116 and 2128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2116 and 2128.

How to find the GCF of 2116 and 2128?

We will first find the prime factorization of 2116 and 2128. After we will calculate the factors of 2116 and 2128 and find the biggest common factor number .

Step-1: Prime Factorization of 2116

Prime factors of 2116 are 2, 23. Prime factorization of 2116 in exponential form is:

2116 = 2² × 23²

Step-2: Prime Factorization of 2128

Prime factors of 2128 are 2, 7, 19. Prime factorization of 2128 in exponential form is:

2128 = 2⁴ × 7¹ × 19¹

Step-3: Factors of 2116

List of positive integer factors of 2116 that divides 2116 without a remainder.

1, 2, 4, 23, 46, 92, 529, 1058

Step-4: Factors of 2128

List of positive integer factors of 2128 that divides 2116 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 56, 76, 112, 133, 152, 266, 304, 532, 1064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2116 and 2128. The biggest common factor number is the GCF number.
So the greatest common factor 2116 and 2128 is 4.

Also check out the Least Common Multiple of 2116 and 2128