Factors of 243
Did you know that 243 is a natural number which is the fifth power of 3? In this lesson, we will calculate the factors of 243, prime factors of 243, and factors of 243 in pairs along with solved examples for a better understanding.
 Factors of 243: 1, 3, 9, 27, 81 and 243
 Prime Factorization of 243: 243 =^{ }3^{5}
1.  What Are the Factors of 243? 
2.  How to Calculate Factors of 243? 
3.  Important Notes 
4.  Factors of 243 by Prime Factorization 
5.  Factors of 243 in Pairs 
6.  Challenging Questions 
What are the Factors of 243?
The factors of 243 are all the numbers that give the value 243 when multiplied. As 243 is odd, it will not have 2 or any multiples of 2 as its factor. To understand why it is composite, let's recall the definition of a composite number.
A number is said to be composite if it has more than two factors.
How to Calculate the Factors of 243?
Let's learn how to calculate the factors of 243. Let's try calculating the factors of 243, starting with the smallest whole number, i.e., 1.
Did it result in the remainder 0?
Yes! So, we will get,
 243 ÷1= 243
 243 ×1= 243
Now try to find out for other whole numbers. As already discussed in the earlier section, even numbers cannot divide 249.
Hence, we only need to check odd numbers.
Thus, the factors of 243 are 1, 3, 9, 27, 81 and 243.
Explore factors using illustrations and interactive examples.
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 30  The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
 Factors of 43  The factors of 43 are 1, 43
 Factors of 32  The factors of 32 are 1, 2, 4, 8, 16, 32
 Factors of 300  The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150
, 300  Factors of 34  The factors of 34 are 1, 2, 17, 34
Important Notes:
 As 243 is an odd number, all its factors will be odd.
 243 is a nonperfect square number. Thus, it will have an even number of factors. This property holds true for every nonperfect square number.
 Factors are never fractions or decimals.
Factors of 243 by Prime Factorization
Prime factorization means to express a composite number as the product of its prime factors. To get the prime factorization of 243, we divide it by its smallest prime factor which is 3.
243/3= 81
Now divide 81 by its smallest prime factor. This process goes on till we get the quotient as 1
The prime factorization of 243 is shown below:
Have you noticed any pattern?
243 = 3 × 81 = 3 × 3 × 3 × 3 × 3 = 243 = 3^{5}
Hence, the factors of 243 are 1, 3, 9, 27, 81 and 243.
Factors of 243 in Pairs
Let's write the factors of 243 in pairs. The pair factors of 243 can be given as below:
Factors  Pair factors 

1 × 243  1, 243 
3 × 81  3, 81 
9 × 27  9, 27 
The abovegiven factors are positive pair factors. The product of two negative numbers also gives a positive number. Hence, it is possible to have negative pair factors as well.
Let's have a look at the negative pair factors.
(1,243), (3, 81), (9, 27)
Challenging Questions:
 Can 0.25 and 1/2 be considered as factors of 243?
Factors of 243 Solved Examples

Example 1: Write all the factors of 243 which are divisible by 3.
Solution:
The factors of 243 are, 1, 3, 9, 27, 81 and 243. We have to find all the factors which are divisible by 3. The divisibility rule of 3 states that a number is divisible by 3 if the sum of all the digits of that number is divisible by 3.
Also, 243 = 3^{5}
The factors of 243 and the multiples of 3 are 3, 9, 27, 81, 243.Hence, 3, 9, 27, 81, and 243 are the factors of 243 which are divisible by 3.

Example 2: Jennifer's teacher gave her 2 numbers, 243 and 217, and asked her to find the common factors for these numbers. Help her find the common factors.
Solution:
Jennifer knows that the factors of 243 are 1, 3, 9, 27, and 243.
She knows 217 can be factored as 217 = 7 × 31.
The factors of 217 are 1, 7, 31 and 217.Hence, Jennifer found 1 is the only common factor among 243 and 217.
FAQs on Factors of 243
What are the factors of 243?
The factors of 243 are 1, 3, 9, 27, 81 and 243
What are the factors of 234?
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234.
What are the prime factors of 243?
The prime factor of 243 is 3.
What is the sum of all factors of 243?
The factors of 243 are 1, 3, 9, 27, 81 and 243. On adding them we get, 1 +3 + 9 + 27 + 81 + 243 = 364
Hence, the sum of factors of 243 is 364.
What are the common factors of 243 and 256?
The factors of 243 are 1, 3, 9, 27, 81 and 243. The factors of 256 are, 1, 2, 4, 8, 16, 32, 64, 128, 256.
Hence, the common factors of 243 and 256 is only 1.
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