Definition of factors of 27: If a number completely divides 27 without leaving a remainder, then that number is called a factor of 27.
By the above definition, we can say that the factors of 27 are the divisors of 27. In this section, we will learn about the factors of 27 and the prime factors of 27.
Table of Contents
Highlights of Factors of 27
- 27=3×3×3 is the prime factorization of 27.
- The factors of 27 are 1, 3, 9 and 27.
- The only prime factor of 27 is 3.
- Negative factors of 27 are –1, -3, -9 and –27.
What are the factors of 27?
Let us write the number 27 multiplicatively in all possible ways. We definitely have:
27 = 1×27
27 = 3×9
As there are no numbers between 3 and 9 that can divide 27, so we will stop right now. So the factors of 27 in pairs are given as follows:
| 27 = a×b | Factors in Pairs (a,b) |
| 27 = 1×27 | (1, 27) |
| 27 = 3×9 | (3, 9) |
Thus the pair factors of 27 are (1, 27) and (3, 9). As all the numbers appearing in pair factors are the factors of 27, we conclude that
|
The factors of 27 are: 1, 3, 9 and 27. |
Number of factors of 27
From above we have calculated the factors of 27 which are 1, 3, 9, and 27. Thus the total number of factors of 27 is four.
Prime Factors of 27
Note that the factors of 27 are 1, 3, 9, and 27. Among those factors, we observe that only 3 is a prime number as 3 does not have any proper divisors.
∴ the only prime factor of 27 is 3.
Question: What are the factors of 27?
Video Solution:
How to find factors of 27?
Now we will determine the factors of 27 by division method. In this method, we will try to find the numbers that can divide 27 with no remainder. See that
27/1=27 and the remainder is 0.
∴ 1 and 27 are factors of 27.
27/3=9 and the remainder is 0.
∴ 3 and 9 are factors of 27.
Note that no numbers other than the numbers in violet color can divide 27. So the numbers in violet color, that is, 1, 3, 9, and 27 are the complete list of factors of 27.
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FAQs on Factors of 27
Ans: As 7 does not divide 27, we say that 7 is not a factor of 27.
Answer: All factors of 27 are 1, 3, 9, and 27.
