What is the Greatest Common Factor of 130 and 138?

Greatest common factor (GCF) of 130 and 138 is 2.

GCF(130,138) = 2

We will now calculate the prime factors of 130 and 138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 130 and 138.

How to find the GCF of 130 and 138?

We will first find the prime factorization of 130 and 138. After we will calculate the factors of 130 and 138 and find the biggest common factor number .

Step-1: Prime Factorization of 130

Prime factors of 130 are 2, 5, 13. Prime factorization of 130 in exponential form is:

130 = 2¹ × 5¹ × 13¹

Step-2: Prime Factorization of 138

Prime factors of 138 are 2, 3, 23. Prime factorization of 138 in exponential form is:

138 = 2¹ × 3¹ × 23¹

Step-3: Factors of 130

List of positive integer factors of 130 that divides 130 without a remainder.

1, 2, 5, 10, 13, 26, 65

Step-4: Factors of 138

List of positive integer factors of 138 that divides 130 without a remainder.

1, 2, 3, 6, 23, 46, 69

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 130 and 138. The biggest common factor number is the GCF number.
So the greatest common factor 130 and 138 is 2.

Also check out the Least Common Multiple of 130 and 138