# Factors of 243

Factors of 243 are 1, 3, 9, 27, 81, and 243

#### How to find factors of a number

 1.   Find factors of 243 using Division Method 2.   Find factors of 243 using Prime Factorization 3.   Find factors of 243 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 243

• Divide 243 by 1: 243 ÷ 1 : Remainder = 0
• Divide 243 by 3: 243 ÷ 3 : Remainder = 0
• Divide 243 by 9: 243 ÷ 9 : Remainder = 0
• Divide 243 by 27: 243 ÷ 27 : Remainder = 0
• Divide 243 by 81: 243 ÷ 81 : Remainder = 0
• Divide 243 by 243: 243 ÷ 243 : Remainder = 0

Hence, Factors of 243 are 1, 3, 9, 27, 81, and 243

#### 2. Steps to find factors of 243 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 243 using the division method, follow these steps:

• Step 1. Start dividing 243 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 243, which is 3. Divide 243 by 3 to obtain the quotient (81).
243 ÷ 3 = 81
• Step 3. Repeat step 1 with the obtained quotient (81).
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 243 is, 243 = 3 x 3 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 243 as shown below:

So, the prime factorization of 243 is, 243 = 3 x 3 x 3 x 3 x 3.

#### 3. Find factors of 243 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 243 would be the two numbers which, when multiplied, give 243 as the result.

The following table represents the calculation of factors of 243 in pairs:

Factor Pair Pair Factorization
1 and 243 1 x 243 = 243
3 and 81 3 x 81 = 243
9 and 27 9 x 27 = 243

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 243. They are called negative pair factors.

Hence, the negative pairs of 243 would be ( -1 , -243 ) , ( -3 , -81 ) and ( -9 , -27 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 243 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 3, 9, 27, 81, 243 are exact divisors of 243.
• Factors of 243 are 1, 3, 9, 27, 81, 243. Each factor divides 243 without leaving a remainder.

• Which is the smallest prime factor of 243?

Smallest prime factor of 243 is 3.

• Is 243 a perfect square?

No 243 is not a perfect square.

• What are five multiples of 243?

First five multiples of 243 are 486, 729, 972, 1215, 1458.

• What is prime factorization of 243?

Prime factorization of 243 is 3 x 3 x 3 x 3 x 3.

• What are factors of 243?

Factors of 243 are 1, 3, 9, 27, 81, 243.

• How do you find factors of a negative number? ( eg. -243 )?

Factors of -243 are -1, -3, -9, -27, -81, -243.

• Is 243 a whole number?

Yes 243 is a whole number.

• Which is greatest factor of 243?

The greatest factor of 243 is 81.

• What are the prime factors of 243?

The factors of 243 are 1, 3, 9, 27, 81, 243.
Prime factors of 243 are 3, 3, 3, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 243. Can you help her?

Prime factors of 243 are 3, 3, 3, 3, 3.
Hence, the product of prime factors of 3.

Can you help Rubel to find out the product of the even factors of 243?

Factors of 243 are 1, 3, 9, 27, 81, 243.
Even factors of 243 are 0.
Hence, product of even factors of 243 is; 0 = 0.

Joy wants to calculate mean of all the factors of 243. Help him in finding the mean of 243.

Factors of 243 are 1, 3, 9, 27, 81, 243.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 243 is 1 + 3 + 9 + 27 + 81 + 243 = 364.
Hence, the mean of factors of 243 is 364 ÷ 6 = 60.67.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 243? Help her in writing all the factors.

Positive factors are 1, 3, 9, 27, 81, 243.
Negative factors are -1, -3, -9, -27, -81, -243.

How many factors are there for 243?

Factors of 243 are 1, 3, 9, 27, 81, 243.
So there are in total 6 factors.

Joey wants to write all the prime factors of 243 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 243 are 3, 3, 3, 3, 3.
So in exponential form it can be written as 35.

Kevin has been asked to write 5 factor(s) of 243. Can you predict the answer?

5 factor(s) of 243 are 1, 3, 9, 27, 81.