Factors of 27 | Prime Factorization of 27 - Explained Simply
Today we are going to present here Factor Tree of 27. The factor is the number that divides the original number. The Factors of 27 are 1, 3, 9 and 27 itself.
What are the factors of 27?
The factors of 27 are all the whole numbers that, when divided into 27, result in a whole number with no remainder. We can also think of them as the whole numbers that multiply together to give 27.
Factor Tree Method of 27: Explained Simply
To find the factors of 27, we systematically check which whole numbers divide 27 evenly, starting from 1.
Start with 1: Every number has 1 as a factor.
1 × 27 = 27
(Factors found: 1, 27)
Check 2: Is 27 divisible by 2? No, because 27 is an odd number (it doesn't end in 0, 2, 4, 6, or 8).
27 ÷ 2 = 13 with a remainder of 1.
Check 3: Is 27 divisible by 3? Yes. A quick trick for divisibility by 3 is to add the digits of the number (2 + 7 = 9). Since 9 is divisible by 3, 27 is also divisible by 3.
3 × 9 = 27
(Factors found: 1, 3, 9, 27)
Check 4: Is 27 divisible by 4? No.
27 ÷ 4 = 6 with a remainder of 3.
Check 5: Is 27 divisible by 5? No, because 27 doesn't end in 0 or 5.
Check 6: Is 27 divisible by 6? No. (If a number is divisible by 6, it must be divisible by both 2 and 3. We already know 27 is not divisible by 2).
27 ÷ 6 = 4 with a remainder of 3.
Check 7: Is 27 divisible by 7? No.
27 ÷ 7 = 3 with a remainder of 6.
Check 8: Is 27 divisible by 8? No.
27 ÷ 8 = 3 with a remainder of 3.
Check 9: We've already found 9 as a factor (3 × 9 = 27). This tells us we've found all the unique pairs. Once you reach a factor that you've already found, or a number whose square is greater than the original number (for 27, √27 ≈ 5.19, so we only need to check up to 5), you can stop.
The positive whole number factors of 27 are 1, 3, 9, and 27.
Prime Factorization of 26
The prime numbers you used as divisors (and the final prime result) are the prime factors.
Step-by-Step: Prime Factorizing 27
Let's apply the division method to find the prime factorization of 27.
Start with the number 27.
`27`
Try dividing by the smallest prime number: 2.
Is 27 divisible by 2? No, because 27 is an odd number. It would leave a remainder.
Try dividing by the next smallest prime number: 3.
Is 27 divisible by 3? Yes! 27 ÷ 3 = 9.
We write down '3' as our first prime factor.
`3 | 27`
` | 9`
Now, we work with the result: 9. Is 9 a prime number? No (its factors are 1, 3, 9).
Try dividing 9 by the smallest prime that divides it evenly.
Is 9 divisible by 2? No.
Is 9 divisible by 3? Yes! 9 ÷ 3 = 3.
We write down '3' as our next prime factor.
`3 | 27`
`3 | 9`
` | 3`
Now, we work with the new result: 3. Is 3 a prime number? Yes!
Since we've reached a prime number, we stop. We've found all the prime building blocks.
`3 | 27`
`3 | 9`
`3 | 3`
| 1
` 1` (We often write 1 at the end to show the process is complete)
Collect all the prime divisors (the numbers on the left): We found 3, 3, and 3.
Write the prime factorization as a product:
`27 = 3 × 3 × 3`
Express in exponential form (for compactness):
Since 3 appears three times, we can write it as 3 raised to the power of 3.
`27 = 3³`
We've successfully broken down the number 27 into its prime building blocks. The prime factorization of 27 is 3 × 3 × 3, which can be written more compactly as 3³. This means that the number 27 is composed solely of the prime number 3, multiplied by itself three times.