What is the Greatest Common Factor of 2128 and 2140?

Greatest common factor (GCF) of 2128 and 2140 is 4.

GCF(2128,2140) = 4

We will now calculate the prime factors of 2128 and 2140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2128 and 2140.

How to find the GCF of 2128 and 2140?

We will first find the prime factorization of 2128 and 2140. After we will calculate the factors of 2128 and 2140 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 2140

Prime factors of 2140 are 2, 5, 107. Prime factorization of 2140 in exponential form is:

2140 = 2² × 5¹ × 107¹

Step-3: Factors of 2128

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

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

Step-4: Factors of 2140

List of positive integer factors of 2140 that divides 2128 without a remainder.

1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2128 and 2140. The biggest common factor number is the GCF number.
So the greatest common factor 2128 and 2140 is 4.

Also check out the Least Common Multiple of 2128 and 2140