Factors of 27 are 1, 3, 9, 27.
Here is complete detailed methods to find the factors of 27.
Actually, Factor is a number which divides any number completely without leaving remainder.
Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then the numbers that we multiply, are the factors of the product.
For example, if we multiply 3 to 9, it gives 27. Here 3 and 9 are called positive factors and if we multiply -1 to -27, it gives 27. So -1 and -27 are called negative factors.
How to Find The Factors of 27 ?
Since factors of 27 are the numbers, which divides 27 completely without leaving remainder. So here we are going to divide 27 by all numbers up to 27. Let’s see the process –
We have to stop the process, if any number of column ‘B’ appears in column ‘A’ or when any element comes in both columns at same level and this element will consider as a factor.
Here we stop the division when 9 appears in column ‘A’, which has already been came in column ‘B’.
Hence, all the factor of 27 in above table 1 are : 1, 3, 9, 27
Similarly, negative factor of 27 are : -1, -3, -9, -27
What Are The Factors of 27 in Pairs ?
As we saw in above table, 1 multiply by 27 gives 27. So (1, 27) is a factor pair of 27. Let us see how many factor pairs can be achieved –
1 x 27 = 27
3 x 9 = 27
9 x 3 = 27
27 x 1 = 27
Similarly, negative factor pairs of 27 can be written as follows –
-1 x -27 = 27
-3 x -9 = 27
-27 x -1 = 27
-9 x -3 = 27
Hence, 27 has 4 factor pairs.
What Are the Prime Factors of 27 ?
The Prime Factors of 27 are 3 & 9. Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.
- Division Method
- Factor Tree Method
Prime Factors of 27 by Division Method
Step 1 : Divide the number by the smallest prime number, which divides the number exactly.
Step 2 : Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the
smallest prime number, choose next smallest prime number.
Step 3 : Repeat Step 2 again and again till the quotient becomes 1.
Step 4 : All the prime numbers used in above process are the prime factors.
Check : Multiply all the prime factors, the multiplication should be the number itself.
Caution : In this method, only prime numbers will be use to divide.
- First of all, we divide 27 by smallest prime number i.e. 2. We didn’t get a whole number as quotient. So try next prime number i.e. 3, we got 9 as quotient and remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
- Divide 9 by prime number 3, we got 3 as quotient.
- Since 3 is a prime number, so 3 will divide by itself only.
- Here we divide 3 by 3 and we got 1 as a quotient.
Hence, 27 = 3 x 3 x 3 = 33
So 27 has only one prime factor i.e. 3.
Factor Tree of 27
Step 1 : Write a number as root of the tree
Step 2 : Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)
Step 3 : Repeat step 2 until we can’t factor any more (or until we got prime factor)
Step 4 : The end nodes are the prime factors.
We can initiate the tree by choosing any two factors. Here we choose 3 and 9 as factors of 27. Further, 9 will split in 3 and 3.
We got the same unique nodes in every tree.
The Factor Tree may be made so many types depends upon choosing the initial and middle factors.
Number of Factors of 27
The Number of Factors of 27 is 4. To find the number of factors, we use Division Method.
In our example, as we saw above 27 = 3 x 3 x 3 = 33
Number of factors is = (power + 1)(power + 1)(power + 1)……….
Hence number of factors of 27 is = (3 + 1) = 4
and if we consider both positive and negative factors, then
total no. of factors = 4 (positive) + 4 (negative) = 8
I hope, this step-by-step tutorial will be helpful to understand factorization method of 27.
What are the factors or divisors of the number 27?
The factors or divisors of the number 27 are 1, 3, 9, 27.
What are the prime factors of the number 27?
The prime factors of the number 27 is 3.
What is the total number of factors of the number 27?
The total number of factors of the number 27 is 4.
What is the total number of prime factors of the number 27?
The total number of prime factors of the number 27 is one.
What is the sum of all factors of the number 27 including 27?
The sum of all the factors of the number 27 including 27 is 30 (i.e 1 + 3 + 9 + 27 = 30)
What is the sum of all factors of the number 27 excluding 27?
The sum of all the factors of the number 27 excluding 27 is 13 (i.e 1 + 3 + 9 = 13)