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The Factors of 27 help in solving fractions and algebraic equations along with understanding the effects of numbers in number theory. Furthermore, knowing the Factors of 27 is important when determining common denominators in fraction operations, finding the Least Common Multiples (LCM), and performing Prime factorization. Read on to learn more in detail about the Factors of 27, their Sum and Factor Tree along with the Factors of Negative 27, and then Factors of 27 in Pairs along with the Division Method.
What are the four Factors of 27?
A Factor of a number is any number that divides into that particular number without any remainder. Thus, when you look at the Factors of 27, they are whole numbers that can be perfectly divided by 27.
27 has only four factors which are 1, 3, 9, and 27 itself.
- Every number is divisible by 1
- 27 ÷ 3 = 9
- 27 ÷ 9 = 3
- 27 ÷ 27 = 1
Thus, these four numbers which are 1, 3, 9, and 27, are the only whole numbers that are the Factors for 27.
Also Read: Factors of 10: Factor Tree, Division Method, Factor Pairs
What is the Sum of Factors of 27?
Now that you know the Factors of 27, it is time to find out the Sum of the Factors of 27:
1 + 3 + 9 + 27 = 40
Hence, the Sum of the Factors of 27 is 40.
Also Read: Factors of 15, Division Method, Factor Pairs and more!
What is the Factor Tree of 27?
A Factor tree is a visual representation that breaks down a number into its Prime factors. Here are the steps to make a Factor tree of 27:
- Begin with 27.
- Divide 27 by its smallest prime factor, which is 3.
- 27 ÷ 3 = 9, so you write 3 and 9.
- Next, you Factor 9 into its Prime factors.
- 9 ÷ 3 = 3, so you write 3 and 3 again.
Thus, the Factor Tree of 27 is as follows:
27
/ \
3 9
/ \
3 3
Therefore, the Prime Factorization of 27 is 3 ✕ 3 ✕ 3 or 33
Also Read: Factors of 16: Negative Factors, Factor Tree, Pairs and Division Method and more!
What are the Factors of Negative 27?
The Factors of Negative Numbers have both positive and negative pairs. When it comes to Negative 27, the factors are similar to those of 27. Therefore, the Factors of -27 are:
- Positive Factors: 1, 3, 9, 27
- Negative Factors: -1, -3, -9, -27
Thus, the entire list of Factors of -27 is -27, -9, -3 and -1
Also Read: Factors of 21: Logic, Sum, Negative Factors, Factor Pairs and more!
Factors of 27 in Pairs
Factors in Pairs are two numbers that multiply together to give the original number. The Factor of 27 in Pairs is as follows:
- 1 ✕ 27 = 27
- 1 ✕ 27 = 27
- 3 ✕ 9 = 27
- 3 ✕ 9 = 27
Thus, the Factor Pairs of 27 are (1, 27) and (3, 9). Likewise, for Negative 27, you need to include the Negative pairs which are:
- −1 ✕ −27 = 27
- −1 ✕ −27 = 27
- −3 ✕ −9 = 27
- −3 ✕ −9 = 27
Hence, the Factor pairs of -27 are (-1, -27) and (-3, -9).
Also Read: Factors of 24: Sum, Factor Tree, Division Method, Factor Pairs
Factors of 27 by Division Method
Another approach to get to know the Factors of 27 is via the Division Method. In this method, you need to manually divide 27 by all the numbers to see which ones leave no remainder. Thus confirming them as Factors.
- Start with 1. When 27 is divided by 1, the result is 27 with no remainder (27 ÷ 27 = 1), so 1 is a Factor.
- Next, try dividing by 2. Since 27 divided by 2 equals 13.5, which is not a whole number, 2 is not a factor.
- Continue with the next number which is 3. Dividing 27 by 3 gives 9 (27 ÷ 3 = 9), which means that 3 is a Factor of 27.
- Check the following numbers in sequence. Dividing 27 by 4, 5, 6, 7, and 8 all result in non-whole numbers, thus these are not factors.
- Finally, divide by 9. Since 27 divided by 9 equals 3 (9 × 3 = 27), 9 is confirmed as a factor.
- Since 27 divided by itself is 1 (27 ÷ 27 = 1), 27 is also a factor.
Thus, using this Division Method helps prove that the Factors of 27 are 1, 3, 9, and 27.
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I hope this helps! Did you like learning about the Factors of 27? You also learn about the Factors of 1 to 25! Also, keep reading our blogs to learn more about the Basic Concepts of Maths!