What is the Greatest Common Factor of 120 and 130?

Greatest common factor (GCF) of 120 and 130 is 10.

GCF(120,130) = 10

We will now calculate the prime factors of 120 and 130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 120 and 130.

How to find the GCF of 120 and 130?

We will first find the prime factorization of 120 and 130. After we will calculate the factors of 120 and 130 and find the biggest common factor number .

Step-1: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 2³ × 3¹ × 5¹

Step-2: 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-3: Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Step-4: Factors of 130

List of positive integer factors of 130 that divides 120 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 120 and 130. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 130 is 10.

Also check out the Least Common Multiple of 120 and 130