# Factors of 216

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216

#### How to find factors of a number

 1.   Find factors of 216 using Division Method 2.   Find factors of 216 using Prime Factorization 3.   Find factors of 216 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 216

• Divide 216 by 1: 216 ÷ 1 : Remainder = 0
• Divide 216 by 2: 216 ÷ 2 : Remainder = 0
• Divide 216 by 3: 216 ÷ 3 : Remainder = 0
• Divide 216 by 4: 216 ÷ 4 : Remainder = 0
• Divide 216 by 6: 216 ÷ 6 : Remainder = 0
• Divide 216 by 8: 216 ÷ 8 : Remainder = 0
• Divide 216 by 9: 216 ÷ 9 : Remainder = 0
• Divide 216 by 12: 216 ÷ 12 : Remainder = 0
• Divide 216 by 18: 216 ÷ 18 : Remainder = 0
• Divide 216 by 24: 216 ÷ 24 : Remainder = 0
• Divide 216 by 27: 216 ÷ 27 : Remainder = 0
• Divide 216 by 36: 216 ÷ 36 : Remainder = 0
• Divide 216 by 54: 216 ÷ 54 : Remainder = 0
• Divide 216 by 72: 216 ÷ 72 : Remainder = 0
• Divide 216 by 108: 216 ÷ 108 : Remainder = 0
• Divide 216 by 216: 216 ÷ 216 : Remainder = 0

Hence, Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216

#### 2. Steps to find factors of 216 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 216 using the division method, follow these steps:

• Step 1. Start dividing 216 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 216, which is 2. Divide 216 by 2 to obtain the quotient (108).
216 ÷ 2 = 108
• Step 3. Repeat step 1 with the obtained quotient (108).
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 216 is, 216 = 2 x 2 x 2 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 216 as shown below:

So, the prime factorization of 216 is, 216 = 2 x 2 x 2 x 3 x 3 x 3.

#### 3. Find factors of 216 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 216 would be the two numbers which, when multiplied, give 216 as the result.

The following table represents the calculation of factors of 216 in pairs:

Factor Pair Pair Factorization
1 and 216 1 x 216 = 216
2 and 108 2 x 108 = 216
3 and 72 3 x 72 = 216
4 and 54 4 x 54 = 216
6 and 36 6 x 36 = 216
8 and 27 8 x 27 = 216
9 and 24 9 x 24 = 216
12 and 18 12 x 18 = 216

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 216. They are called negative pair factors.

Hence, the negative pairs of 216 would be ( -1 , -216 ) , ( -2 , -108 ) , ( -3 , -72 ) , ( -4 , -54 ) , ( -6 , -36 ) , ( -8 , -27 ) , ( -9 , -24 ) and ( -12 , -18 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 216 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 216.
• Every number is a factor of zero (0), since 216 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, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216 are exact divisors of 216.
• Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. Each factor divides 216 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216 are all less than or equal to 216.

• Which is the smallest prime factor of 216?

Smallest prime factor of 216 is 2.

• Is 216 a perfect square?

No 216 is not a perfect square.

• What are five multiples of 216?

First five multiples of 216 are 432, 648, 864, 1080, 1296.

• What is prime factorization of 216?

Prime factorization of 216 is 2 x 2 x 2 x 3 x 3 x 3.

• What are factors of 216?

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.

• How do you find factors of a negative number? ( eg. -216 )?

Factors of -216 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -108, -216.

• Is 216 a whole number?

Yes 216 is a whole number.

• Which is greatest factor of 216?

The greatest factor of 216 is 108.

• What are the prime factors of 216?

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
Prime factors of 216 are 2, 2, 2, 3, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 216. Can you help her?

Prime factors of 216 are 2, 2, 2, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 216?

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
Even factors of 216 are 2, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 216.
Hence, product of even factors of 216 is; 2 x 4 x 6 x 8 x 12 x 18 x 24 x 36 x 54 x 72 x 108 x 216 = 6499837226778624.

Joy wants to calculate mean of all the factors of 216. Help him in finding the mean of 216.

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 216 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 + 216 = 600.
Hence, the mean of factors of 216 is 600 ÷ 16 = 37.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 216? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -108, -216.

How many factors are there for 216?

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216.
So there are in total 16 factors.

Joey wants to write all the prime factors of 216 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 216 are 2, 2, 2, 3, 3, 3.
So in exponential form it can be written as 23 x 33.

Kevin has been asked to write 15 factor(s) of 216. Can you predict the answer?

15 factor(s) of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108.