Factors are an important concept in arithmetic. Factors of 27 are simply numbers — more than two, which upon multiplication lead to the result or product of 27. In simple terms, factors are two or more numbers which upon multiplication lead to another number. Factors are also explored in algebra. Since algebra uses variables most of the time, the factors of an algebraic term are also in the form of variables. Factors of 27 are specifically unique in its nature. Understanding its factors through division, prime factorization is some key takeaways from this article.
The example below can explain this further:
(x2 + 5x + 5) is an algebraic term with two factors (x+5) and (x+ 1)
(x+5)(x+ 1) = x2 + 5x + 5
As mentioned at the beginning of this article, Factors of 27 are simply numbers, more than two, which upon multiplication lead to the result or product of 27. Other important concepts for solving for factors are prime numbers, multiplication tables up to 20, negative and positive numbers.
Let's discover the factors of 27 through the division method.
Starting from the smallest number, let's find the common factors 27 by division method:
27 ÷ 1 = 27 |
27 ÷ 2 = not divisible |
27 ÷ 3 = 9 |
27 ÷ 4 = not divisible |
27 ÷ 5 = not divisible |
27 ÷ 6 = not divisible |
27 ÷ 7 = not divisible |
27 ÷ 8 = not divisible |
27 ÷ 9 = 3 |
27 ÷ 10 = not divisible |
27 ÷ 11 = not divisible |
27 ÷ 12 = not divisible |
27 ÷ 13 = not divisible |
27 ÷ 14 = not divisible |
27 ÷ 15 = not divisible |
27 ÷ 16 = not divisible |
27 ÷ 17 = not divisible |
27 ÷ 18 = not divisible |
27 ÷ 19 = not divisible |
27 ÷ 20 = not divisible |
Following the multiplication tables up to 20, we can easily find the factors of 27.
The factors of 27 obtained are 3, 9, 27.
In order to know more factors of 27, we can start dividing 27 with the factors that we have obtained until now.
27 ÷ 27 = 1 |
27 ÷ 9 = 3 |
27 ÷ 3 = 9 |
With the above method, we have found 1 more new factor of 27 that is 1. The common factors for 27 are 3 and 9.
Therefore the total number of factors that 27 has is 4 and they are 1, 3, 9, and 27.
A frequently asked question (FAQ) is whether a number can have a factor bigger than the number itself. The answer to that is no. Since factors are a multiplication of numbers that lead to another number, the factors are always smaller than the product.
A number itself is its greatest factor. The biggest factor for 27 is 27 itself. The value of the factor never exceeds the product value.
Pairs of factors is another approach of finding factors of a number. The pairs of factors for 27 can be derived from the single factors that we have found above: 1, 3, 9, and 27.
Use the approach below in order to understand the methodology behind a pair of two factors:
1 x 27 = 27 |
3 x 9 = 27 |
From the calculation above, it can be inferred that there are 2 pairs of two factors for 27. They are (1, 27) and (3, 9). You can observe that these pairs of factors have been derived originally from the factors obtained through division. Therefore, it is highly recommended that you use the division approach when attempting questions on factors.
Just as there are pairs of two factors, there are also pairs of three and more factors for a product. This approach is used to find the smallest factors of 27. Similar to pairs of two factors, we will be using the factors derived from the division method: 1, 3, 9, and 27.
1 x 3 x 9 = 27 |
From the calculations above, we can see that there can be a pair of three factors for 27, and they are (1, 3, 9).
1. Give some examples of prime factors.
Answer: Prime numbers are the numbers that are divisible by 1 one and the number itself. 2 is a prime number which is the product of 1 and 2 (the number itself). Remember, that 1 is not a prime number.
Some other examples of prime numbers are 3, 5, 7, etc. These numbers do not have any other factors except for 1 and the number itself.
2. Show the prime factorization method to find the factors of 27. Can factors be negative? Find negative factors of 27.
Answer: A prime number is a number which is the product of 1 and the number itself.
Factors can be positive and negative numbers. This means that a positive product can also be obtained with the multiplication of two negative factors. By simply adding the negative sign for each factor, you can get a positive product with negative factors. It can be put as follow:
Therefore the factors for 27 can also be a pair of two factors such as (-1, -27) and (-3, -9)
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