# Factors of 396

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

#### How to find factors of a number

 1.   Find factors of 396 using Division Method 2.   Find factors of 396 using Prime Factorization 3.   Find factors of 396 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 396

• Divide 396 by 1: 396 ÷ 1 : Remainder = 0
• Divide 396 by 2: 396 ÷ 2 : Remainder = 0
• Divide 396 by 3: 396 ÷ 3 : Remainder = 0
• Divide 396 by 4: 396 ÷ 4 : Remainder = 0
• Divide 396 by 6: 396 ÷ 6 : Remainder = 0
• Divide 396 by 9: 396 ÷ 9 : Remainder = 0
• Divide 396 by 11: 396 ÷ 11 : Remainder = 0
• Divide 396 by 12: 396 ÷ 12 : Remainder = 0
• Divide 396 by 18: 396 ÷ 18 : Remainder = 0
• Divide 396 by 22: 396 ÷ 22 : Remainder = 0
• Divide 396 by 33: 396 ÷ 33 : Remainder = 0
• Divide 396 by 36: 396 ÷ 36 : Remainder = 0
• Divide 396 by 44: 396 ÷ 44 : Remainder = 0
• Divide 396 by 66: 396 ÷ 66 : Remainder = 0
• Divide 396 by 99: 396 ÷ 99 : Remainder = 0
• Divide 396 by 132: 396 ÷ 132 : Remainder = 0
• Divide 396 by 198: 396 ÷ 198 : Remainder = 0
• Divide 396 by 396: 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

#### 2. Steps to find factors of 396 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 396 using the division method, follow these steps:

• Step 1. Start dividing 396 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 396, which is 2. Divide 396 by 2 to obtain the quotient (198).
396 ÷ 2 = 198
• Step 3. Repeat step 1 with the obtained quotient (198).
198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1

So, the prime factorization of 396 is, 396 = 2 x 2 x 3 x 3 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 396 as shown below:

So, the prime factorization of 396 is, 396 = 2 x 2 x 3 x 3 x 11.

#### 3. Find factors of 396 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 396 would be the two numbers which, when multiplied, give 396 as the result.

The following table represents the calculation of factors of 396 in pairs:

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 ) , ( -2 , -198 ) , ( -3 , -132 ) , ( -4 , -99 ) , ( -6 , -66 ) , ( -9 , -44 ) , ( -11 , -36 ) , ( -12 , -33 ) and ( -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.

• Which is the smallest prime factor of 396?

Smallest prime factor of 396 is 2.

• Is 396 a perfect square?

No 396 is not a perfect square.

• What are five multiples of 396?

First five multiples of 396 are 792, 1188, 1584, 1980, 2376.

• What is prime factorization of 396?

Prime factorization of 396 is 2 x 2 x 3 x 3 x 11.

• What are 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.

• How do you find factors of a negative number? ( eg. -396 )?

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

• Is 396 a whole number?

Yes 396 is a whole number.

• Which is greatest factor of 396?

The greatest factor of 396 is 198.

• What are the prime factors of 396?

The 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.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 396. Can you help her?

Prime factors of 396 are 2, 2, 3, 3, 11.
Hence, the product of prime factors of 66.

Can you help Rubel to find out the product of the even 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.
Even factors of 396 are 2, 4, 6, 12, 18, 22, 36, 44, 66, 132, 198, 396.
Hence, product of even factors of 396 is; 2 x 4 x 6 x 12 x 18 x 22 x 36 x 44 x 66 x 132 x 198 x 396 = 246803372284575740.

Joy wants to calculate mean of all the factors of 396. Help him in finding the mean of 396.

Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 396 is 1 + 2 + 3 + 4 + 6 + 9 + 11 + 12 + 18 + 22 + 33 + 36 + 44 + 66 + 99 + 132 + 198 + 396 = 1092.
Hence, the mean of factors of 396 is 1092 ÷ 18 = 60.67.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 396? Help her in writing all the factors.

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

How many factors are there for 396?

Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.
So there are in total 18 factors.

Joey wants to write all the prime factors of 396 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 396 are 2, 2, 3, 3, 11.
So in exponential form it can be written as 22 x 32 x 11.

Kevin has been asked to write 17 factor(s) of 396. Can you predict the answer?

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