[Maths Class Notes] on Factors of 216 Pdf for Exam

Factors can be defined as numbers which can divide a parent number completely without leaving any remainder. For instance, the factors of the number 9 are 1 and 3 1×9=9, 3×3=9

1×9=9, 3×3=9. So let us begin discussing the most fundamental of questions “what are the factors of 216?” In this particular article we will identify all the factors of 216 and will also analyze, scrutinize, and highlight the methods that are utilized to find out the factors of 216. Students can adopt the techniques mentioned below to analyze the factors of other numbers as well.

Factors are numbers that can divide a parent number completely without leaving any remainder. For example, factors of the number 9 are 1 and 3 1×9=9, 3×3=9, 1×9=9, 3×3=9 1 x 9 = 9, 3 x 3 = 9. 

 

The prime factorization has two methods, namely the division method and the factor tree method, and we can identify the Factors of 216 using any one of the two methods.

What are the Factors of 216?

There are 2 methods of prime factorization. They are the division method and the factor tree method. Identify the Factors of 216 using any one of the two methods. 

1. Division Method

In this method, the first step is about dividing the number by the smallest prime number available. Next, divide the resulting number with the smallest prime number. Repeat this process until you get the number that cannot be factored further. 

Follow the given steps to find out the factors of 216. 

216 ÷ 2 = 108

Further, divide the number 108 with the smallest prime number

108 ÷ 2 = 54

54 is further divided with the smallest prime number i.e. 2

54 ÷ 2 = 27

Divide 27 with the smallest prime number i.e. 3

27 ÷ 3 = 9

9 is further divided with the smallest prime number

9 ÷ 3 = 3

3 is further divided

3 ÷ 3 =1

1 cannot be further divided

The prime factors of 216 are 2×2×2×3×3×3. They are written as 23 × 33.

Let us now analyze another method to answer the question of “what are the factors of 216?”

2. Factor Tree Method

In this method, the factor tree method, we need to identify the initial factor pair of the given number. These factor pairs are known as the branches of the factor tree.

The next step is to identify the factor pairs of the branches. Further sub-branches are produced. 

Repeat this same process until you arrive at the number that is not factored further.

Write down the prime numbers which are the factors for the given number.

With the help of either of these two methods, we can get the factor pairs. The two methods apply for both the small and the large numbers like 120, 216, 524, 1028, 2024, 5000 etc.

• We can find the factors of 216 using the factor tree method. Follow the given steps.

• Write the pair of factors of 216 and the branches of the tree. 

• The initial factor pairs of 216 are 2 and 108 (branches)

• As 2 is a prime number, it cannot be factored further. We can factorize 108.

• Write the factor pairs of 108. 

• The initial factor pairs of 108 are 2 and 54.

• Factorize 54 to get other factors of 216.

• Factor pairs of 54 are 2 and 27.

• 27 is factored further. Factors of 27 are 3 x 3 x 3 which can be denoted as 33.

• What are all the factors of 216? Writing all factors of 216 together, we get 2×2×2×3×3×3.

Prime Factorization of 216

Here is the representation of the factor tree to find 216 prime factorization

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One can find the prime factorization of 216 using any one of the above steps. 

What are the Factor Pairs of 216?

A factor pair is a pair of numbers that on multiplication produce the given number. For any given number, we can have positive and negative factor pairs.

Note: The factor pairs are usually positive. No negative factor pairs are found generally. 

The factor pairs of 216 are: 

1. Positive Factor Pairs:

• 2 × 108.

• 3 × 54.

• 4 × 72.

• 6 × 36.

• 8 × 27.

• 9 × 24.

• 12 × 18. 

On multiplying the above pairs of numbers, we get 216.

The positive factor pairs are (2, 108) (3, 54) (4, 72) (6, 36) (8, 27) (9, 24) (12, 18).

 

2. Negative Factor Pairs:

• -2 × -108.

• -3 × -54.

• -4 × -72.

• -6 × -36.

• -8 × -27.

• -9 × -24.

• -12 × -18. 

On multiplying the above pairs of numbers, we get 216.

The negative factor pairs are (-2, -108) (-3, -54) (-4, -72) (-6, -36) (-8, -27) (-9, -24) (-12, -18). 

The total number of factor pairs of 216 is 14 out of which 7 are positive and 7 are negative.  

What are the Different Methods of Prime Factorization?

Division Method:

• The first step involves dividing the number by the smallest prime number. Again, divide the resulting number with the smallest prime number. Repeat the process till you get the number that cannot be factored further. 

• Write down all the factors used in this division process. These are the factors of the given number.

 

Factor Tree Method:

• In the factor tree method, identify the initial factor pair of the given number. These factor pairs are considered as branches of the factor tree. 

• Identify the factor pairs of the branches. Further sub-branches are produced. 

• Repeat the same process till you arrive at the number that is not factored further. 

• Write the prime numbers together which are the factors for the given number. 

By performing either of the two methods, factor pairs are obtained for the given number. These methods apply for small and large numbers like 120, 216, 524, 1028, 2024, 5000 etc.