# Factors of 396 in pair

Factors of 396 in pair are (1, 396) , (2, 198) , (3, 132) , (4, 99) , (6, 66) , (9, 44) , (11, 36) , (12, 33) and (18, 22)

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

 1.   Steps to find factors of 396 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 396 in pair

Factor Pair Pair Factorization
1 and 396 1 x 396 = 396
2 and 198 2 x 198 = 396
3 and 132 3 x 132 = 396
4 and 99 4 x 99 = 396
6 and 66 6 x 66 = 396
9 and 44 9 x 44 = 396
11 and 36 11 x 36 = 396
12 and 33 12 x 33 = 396
18 and 22 18 x 22 = 396

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 396. They are called negative pair factors.

Hence, the negative pairs of 396 would be ( -1 , -396 ) .

#### 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 396 are 1 , 2 , 3 , 4 , 6 , 9 , 11 , 12 , 18 , 22 , 33 , 36 , 44 , 66 , 99 , 132 , 198 , 396. So, factors of 396 in pair are (1,396), (2,198), (3,132), (4,99), (6,66), (9,44), (11,36), (12,33), (18,22).

#### 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. 396 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 396.
• Every number is a factor of zero (0), since 396 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, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 are exact divisors of 396.
• Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396. Each factor divides 396 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 are all less than or equal to 396.

#### Steps to find Factors of 396

• Step 1. Find all the numbers that would divide 396 without leaving any remainder. Starting with the number 1 upto 198 (half of 396). The number 1 and the number itself are always factors of the given number.
396 ÷ 1 : Remainder = 0
396 ÷ 2 : Remainder = 0
396 ÷ 3 : Remainder = 0
396 ÷ 4 : Remainder = 0
396 ÷ 6 : Remainder = 0
396 ÷ 9 : Remainder = 0
396 ÷ 11 : Remainder = 0
396 ÷ 12 : Remainder = 0
396 ÷ 18 : Remainder = 0
396 ÷ 22 : Remainder = 0
396 ÷ 33 : Remainder = 0
396 ÷ 36 : Remainder = 0
396 ÷ 44 : Remainder = 0
396 ÷ 66 : Remainder = 0
396 ÷ 99 : Remainder = 0
396 ÷ 132 : Remainder = 0
396 ÷ 198 : Remainder = 0
396 ÷ 396 : Remainder = 0

Hence, Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, and 396

• Is 396 a composite number?

Yes 396 is a composite number.

• Is 396 a prime number?

No 396 is not a prime number.

• What is the mean of factors of 396?

Factors of 396 are 1 , 2 , 3 , 4 , 6 , 9 , 11 , 12 , 18 , 22 , 33 , 36 , 44 , 66 , 99 , 132 , 198 , 396. therefore mean of factors of 396 is (1 + 2 + 3 + 4 + 6 + 9 + 11 + 12 + 18 + 22 + 33 + 36 + 44 + 66 + 99 + 132 + 198 + 396) / 18 = 60.67.

• 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

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 396.
- Writing all prime factors of 396.
- Writing all the possible factors of 396 in pair.
Help him in writing all these.

Positive factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.
Prime factors of 396 are 2, 2, 3, 3, 11.
Factors of 396 in pair are (1,396), (2,198), (3,132), (4,99), (6,66), (9,44), (11,36), (12,33), (18,22).

What are the pair factors of 396?

Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396. Hence, the factors of 396 in pair are (1,396), (2,198), (3,132), (4,99), (6,66), (9,44), (11,36), (12,33), (18,22).

Can you help Sammy list the factors of 396 and also find the factor pairs?

Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.
Factors of 396 in pair are (1,396), (2,198), (3,132), (4,99), (6,66), (9,44), (11,36), (12,33), (18,22).

The area of a rectangle is 396 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 396 in pair. So, the possible combinations (1,396), (2,198), (3,132), (4,99), (6,66), (9,44), (11,36), (12,33), (18,22).

Help Diji in finding factors of 396 by Prime Factorization method and then sorting factors of 396 in pairs.

Prime factorization of 396 is 2 x 2 x 3 x 3 x 11. Factors of 396 in pair can be written as (1,396), (2,198), (3,132), (4,99), (6,66), (9,44), (11,36), (12,33), (18,22).

Write the smallest prime factor of 396.

Smallest prime factor of 396 is 2.

Write the largest prime factor of 396.

Largest prime factor of 396 is 11.

Diji wants to write all the negative factors of 396. Can you help Diji in doing the same?

Negative factors of 396 are -1, -2, -3, -4, -6, -9, -11, -12, -18, -22, -33, -36, -44, -66, -99, -132, -198, -396.