What is the Greatest Common Factor of 2125 and 2142?

Greatest common factor (GCF) of 2125 and 2142 is 17.

GCF(2125,2142) = 17

We will now calculate the prime factors of 2125 and 2142, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2125 and 2142.

How to find the GCF of 2125 and 2142?

We will first find the prime factorization of 2125 and 2142. After we will calculate the factors of 2125 and 2142 and find the biggest common factor number .

Step-1: Prime Factorization of 2125

Prime factors of 2125 are 5, 17. Prime factorization of 2125 in exponential form is:

2125 = 5³ × 17¹

Step-2: Prime Factorization of 2142

Prime factors of 2142 are 2, 3, 7, 17. Prime factorization of 2142 in exponential form is:

2142 = 2¹ × 3² × 7¹ × 17¹

Step-3: Factors of 2125

List of positive integer factors of 2125 that divides 2125 without a remainder.

1, 5, 17, 25, 85, 125, 425

Step-4: Factors of 2142

List of positive integer factors of 2142 that divides 2125 without a remainder.

1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2125 and 2142. The biggest common factor number is the GCF number.
So the greatest common factor 2125 and 2142 is 17.

Also check out the Least Common Multiple of 2125 and 2142