What is the Greatest Common Factor of 270 and 282?

Greatest common factor (GCF) of 270 and 282 is 6.

GCF(270,282) = 6

We will now calculate the prime factors of 270 and 282, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 270 and 282.

How to find the GCF of 270 and 282?

We will first find the prime factorization of 270 and 282. After we will calculate the factors of 270 and 282 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 282

Prime factors of 282 are 2, 3, 47. Prime factorization of 282 in exponential form is:

282 = 2¹ × 3¹ × 47¹

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 282

List of positive integer factors of 282 that divides 270 without a remainder.

1, 2, 3, 6, 47, 94, 141

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 270 and 282. The biggest common factor number is the GCF number.
So the greatest common factor 270 and 282 is 6.

Also check out the Least Common Multiple of 270 and 282