What is the Greatest Common Factor of 270 and 290?

Greatest common factor (GCF) of 270 and 290 is 10.

GCF(270,290) = 10

We will now calculate the prime factors of 270 and 290, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 270 and 290.

How to find the GCF of 270 and 290?

We will first find the prime factorization of 270 and 290. After we will calculate the factors of 270 and 290 and find the biggest common factor number .

Step-1: Prime Factorization of 270

Prime factors of 270 are 2, 3, 5. Prime factorization of 270 in exponential form is:

270 = 2¹ × 3³ × 5¹

Step-2: Prime Factorization of 290

Prime factors of 290 are 2, 5, 29. Prime factorization of 290 in exponential form is:

290 = 2¹ × 5¹ × 29¹

Step-3: Factors of 270

List of positive integer factors of 270 that divides 270 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135

Step-4: Factors of 290

List of positive integer factors of 290 that divides 270 without a remainder.

1, 2, 5, 10, 29, 58, 145

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 270 and 290. The biggest common factor number is the GCF number.
So the greatest common factor 270 and 290 is 10.

Also check out the Least Common Multiple of 270 and 290