What is the Greatest Common Factor of 2114 and 2132?

Greatest common factor (GCF) of 2114 and 2132 is 2.

GCF(2114,2132) = 2

We will now calculate the prime factors of 2114 and 2132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2114 and 2132.

How to find the GCF of 2114 and 2132?

We will first find the prime factorization of 2114 and 2132. After we will calculate the factors of 2114 and 2132 and find the biggest common factor number .

Step-1: Prime Factorization of 2114

Prime factors of 2114 are 2, 7, 151. Prime factorization of 2114 in exponential form is:

2114 = 2¹ × 7¹ × 151¹

Step-2: Prime Factorization of 2132

Prime factors of 2132 are 2, 13, 41. Prime factorization of 2132 in exponential form is:

2132 = 2² × 13¹ × 41¹

Step-3: Factors of 2114

List of positive integer factors of 2114 that divides 2114 without a remainder.

1, 2, 7, 14, 151, 302, 1057

Step-4: Factors of 2132

List of positive integer factors of 2132 that divides 2114 without a remainder.

1, 2, 4, 13, 26, 41, 52, 82, 164, 533, 1066

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2114 and 2132. The biggest common factor number is the GCF number.
So the greatest common factor 2114 and 2132 is 2.

Also check out the Least Common Multiple of 2114 and 2132