# Factors of 324

Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324

#### How to find factors of a number

 1.   Find factors of 324 using Division Method 2.   Find factors of 324 using Prime Factorization 3.   Find factors of 324 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 324

• Divide 324 by 1: 324 ÷ 1 : Remainder = 0
• Divide 324 by 2: 324 ÷ 2 : Remainder = 0
• Divide 324 by 3: 324 ÷ 3 : Remainder = 0
• Divide 324 by 4: 324 ÷ 4 : Remainder = 0
• Divide 324 by 6: 324 ÷ 6 : Remainder = 0
• Divide 324 by 9: 324 ÷ 9 : Remainder = 0
• Divide 324 by 12: 324 ÷ 12 : Remainder = 0
• Divide 324 by 18: 324 ÷ 18 : Remainder = 0
• Divide 324 by 27: 324 ÷ 27 : Remainder = 0
• Divide 324 by 36: 324 ÷ 36 : Remainder = 0
• Divide 324 by 54: 324 ÷ 54 : Remainder = 0
• Divide 324 by 81: 324 ÷ 81 : Remainder = 0
• Divide 324 by 108: 324 ÷ 108 : Remainder = 0
• Divide 324 by 162: 324 ÷ 162 : Remainder = 0
• Divide 324 by 324: 324 ÷ 324 : Remainder = 0

Hence, Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324

#### 2. Steps to find factors of 324 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 324 using the division method, follow these steps:

• Step 1. Start dividing 324 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 324, which is 2. Divide 324 by 2 to obtain the quotient (162).
324 ÷ 2 = 162
• Step 3. Repeat step 1 with the obtained quotient (162).
162 ÷ 2 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 324 is, 324 = 2 x 2 x 3 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 324 as shown below:

So, the prime factorization of 324 is, 324 = 2 x 2 x 3 x 3 x 3 x 3.

#### 3. Find factors of 324 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 324 would be the two numbers which, when multiplied, give 324 as the result.

The following table represents the calculation of factors of 324 in pairs:

Factor Pair Pair Factorization
1 and 324 1 x 324 = 324
2 and 162 2 x 162 = 324
3 and 108 3 x 108 = 324
4 and 81 4 x 81 = 324
6 and 54 6 x 54 = 324
9 and 36 9 x 36 = 324
12 and 27 12 x 27 = 324
18 and 18 18 x 18 = 324

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 324. They are called negative pair factors.

Hence, the negative pairs of 324 would be ( -1 , -324 ) , ( -2 , -162 ) , ( -3 , -108 ) , ( -4 , -81 ) , ( -6 , -54 ) , ( -9 , -36 ) , ( -12 , -27 ) and ( -18 , -18 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 324 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 324.
• Every number is a factor of zero (0), since 324 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, 12, 18, 27, 36, 54, 81, 108, 162, 324 are exact divisors of 324.
• Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324. Each factor divides 324 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324 are all less than or equal to 324.

• Which is the smallest prime factor of 324?

Smallest prime factor of 324 is 2.

• Is 324 a perfect square?

Yes 324 is a perfect square.

• What are five multiples of 324?

First five multiples of 324 are 648, 972, 1296, 1620, 1944.

• What is prime factorization of 324?

Prime factorization of 324 is 2 x 2 x 3 x 3 x 3 x 3.

• What are factors of 324?

Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.

• How do you find factors of a negative number? ( eg. -324 )?

Factors of -324 are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -324.

• Is 324 a whole number?

Yes 324 is a whole number.

• Which is greatest factor of 324?

The greatest factor of 324 is 162.

• What are the prime factors of 324?

The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
Prime factors of 324 are 2, 2, 3, 3, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 324. Can you help her?

Prime factors of 324 are 2, 2, 3, 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 324?

Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
Even factors of 324 are 2, 4, 6, 12, 18, 36, 54, 108, 162, 324.
Hence, product of even factors of 324 is; 2 x 4 x 6 x 12 x 18 x 36 x 54 x 108 x 162 x 324 = 114254951251968.

Joy wants to calculate mean of all the factors of 324. Help him in finding the mean of 324.

Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 324 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 324 = 847.
Hence, the mean of factors of 324 is 847 ÷ 15 = 56.47.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 324? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -324.

How many factors are there for 324?

Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
So there are in total 15 factors.

Joey wants to write all the prime factors of 324 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 324 are 2, 2, 3, 3, 3, 3.
So in exponential form it can be written as 22 x 34.

Kevin has been asked to write 14 factor(s) of 324. Can you predict the answer?

14 factor(s) of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162.