# Factors of 216 in pair

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

#### How to find factors of a number in pair

 1.   Steps to find factors of 216 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 216 in pair

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 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 216 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 27 , 36 , 54 , 72 , 108 , 216. So, factors of 216 in pair are (1,216), (2,108), (3,72), (4,54), (6,36), (8,27), (9,24), (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.

#### Steps to find Factors of 216

• Step 1. Find all the numbers that would divide 216 without leaving any remainder. Starting with the number 1 upto 108 (half of 216). The number 1 and the number itself are always factors of the given number.
216 ÷ 1 : Remainder = 0
216 ÷ 2 : Remainder = 0
216 ÷ 3 : Remainder = 0
216 ÷ 4 : Remainder = 0
216 ÷ 6 : Remainder = 0
216 ÷ 8 : Remainder = 0
216 ÷ 9 : Remainder = 0
216 ÷ 12 : Remainder = 0
216 ÷ 18 : Remainder = 0
216 ÷ 24 : Remainder = 0
216 ÷ 27 : Remainder = 0
216 ÷ 36 : Remainder = 0
216 ÷ 54 : Remainder = 0
216 ÷ 72 : Remainder = 0
216 ÷ 108 : Remainder = 0
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

• Is 216 a composite number?

Yes 216 is a composite number.

• Is 216 a prime number?

No 216 is not a prime number.

• What is the mean of factors of 216?

Factors of 216 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 27 , 36 , 54 , 72 , 108 , 216. therefore mean of factors of 216 is (1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 + 216) / 16 = 37.50.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Ariel has been asked to write all factor pairs of 216 but she is finding it difficult. Can you help her find out?

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

Sammy wants to write all the negative factors of 216 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 216 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -108, -216. Hence, factors of 216 in pair are (-1,-216), (-2,-108), (-3,-72), (-4,-54), (-6,-36), (-8,-27), (-9,-24), (-12,-18).

Help Deep in writing the positive factors of 216 in pair and negative factor of 216 in pair.

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. Positive factors of 216 in pair are (1,216), (2,108), (3,72), (4,54), (6,36), (8,27), (9,24), (12,18). Negative factors of 216 in pair are (-1,-216), (-2,-108), (-3,-72), (-4,-54), (-6,-36), (-8,-27), (-9,-24), (-12,-18).

Find the product of all factors of 216.

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. So the product of all factors of 216 would be 1 x 2 x 3 x 4 x 6 x 8 x 9 x 12 x 18 x 24 x 27 x 36 x 54 x 72 x 108 x 216 = 4738381338321617000.

Find the product of all prime factors of 216.

Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. Prime factors are 2, 2, 2, 3, 3, 3. So, the product of all prime factors of 216 would be 2 x 2 x 2 x 3 x 3 x 3 = 216.

Can you help Sammy list the factors of 216 and also find the factor pairs?

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

Sammy has 216 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 216 blocks in all possible ways to form a rectangle, we need to calculate factors of 216 in pair. Therefore, factors of 216 in pair are (1,216), (2,108), (3,72), (4,54), (6,36), (8,27), (9,24), (12,18)