What is the prime factorization of 270?

To find the prime factorization of 270, we start by dividing it by the smallest prime number, which is 2. Since 270 is even, we can divide:

• 270 ÷ 2 = 135

Now, we need to factor 135. The next smallest prime number is 3. Since the sum of the digits of 135 (1 + 3 + 5 = 9) is divisible by 3, we can divide 135 by 3:

• 135 ÷ 3 = 45

Next, we factor 45. Again, we can divide by 3 (since 4 + 5 = 9, which is also divisible by 3):

• 45 ÷ 3 = 15

Now we factor 15, and since it’s also divisible by 3, we divide:

• 15 ÷ 3 = 5

Finally, 5 is a prime number. So we stop here. Now we can put it all together:

The prime factorization of 270 is:

• 2 × 3 × 3 × 3 × 5

Alternatively, we can express this using exponents:

270 = 2 × 3³ × 5