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Factors of 324: Prime Factorization, Methods, and Example

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What Are the Factors of 324?
How To Find the Factors of 324?
- Total Number of Factors of 324
- Important Notes
Factors of 324 by Prime Factorization
Factors of 324 in Pairs
Factors of 324 Solved Examples
- Example 1
- Solution
- Example 2
- Solution

Factors of 324: Prime Factorization, Methods, and Examples

The factors of 324聽are numbers that divide 324 into even proportions without leaving any remainder. The factors of 324 can be positive and negative.聽

The number 324 is an even composite, which indicates that it has more than two factors.

What Are the Factors of 324?

The factors of 324 are聽1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324. These numbers are the factors as they do not leave any remainder when divided by 324.

The factors of 324聽are classified as prime numbers and composite numbers. The prime factors of the number 324 can be determined using the prime factorization technique.

How To Find the Factors of 324?

You can find the factors of 324聽by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 324, create a list containing the numbers that are exactly divisible by 324 with zero remainders. One important thing to note is that 1 and 324 are 324’s factors, as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 324 are determined as follows:

\[\dfrac{324}{1} = 324\]

\[\dfrac{324}{2} = 162\]

\[\dfrac{324}{3} = 108\]

\[\dfrac{324}{4} = 81\]

\[\dfrac{324}{6} = 54\]

\[\dfrac{324}{9} = 36\]

\[\dfrac{324}{12} = 27\]

\[\dfrac{324}{18} = 18\]

\[\dfrac{324}{324} = 1\]

Therefore,1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324聽are the factors of 324.

Total Number of Factors of 324

For 324, there are fifteen聽positive factors and fifteen聽negative ones. So in total, there are thirty factors of 324.聽

To find the total number of factors of the given number, follow the procedure mentioned below:

Find the factorization/prime factorization of the given number.
Demonstrate the prime factorization of the number in the form of exponent form.
Add 1 to each of the exponents of the prime factor.
Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of X is given as:

Factorization of X is聽1 x 2$^2$ x 3$^4$.

The exponent of 1 is 1, and the exponent of 2 is 2. Also, the exponent of 3 is 4.

Adding 1 to each and multiplying them together results in m.

Therefore, the total number of factors of 324 is 30. Fifteen are positive, and fifteen factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

The factor of any given number must be a whole number.
The factors of the number cannot be in the form of decimals or fractions.
Factors can be positive as well as negative.
Negative factors are the additive inverse of the positive factors of a given number.
The factor of a number cannot be greater than that number.
Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 324 by Prime Factorization

The number 324聽is a composite. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 324 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 324, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 324聽can be expressed as:

324 = 2$^2$ x 3$^4$

Factors of 324 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 324, the factor pairs can be found as:

The possible factor pairs of 324聽are given as聽(1, 324), (2, 162), (3, 108), (4, 81), (6, 54), (9, 36), (12, 27),聽and (18, 18).

All these numbers in pairs, when multiplied, give 324 as the product.

The negative factor pairs of 324 are given as:

-12 x -27 = 324聽聽

聽-18 x -18 = 324聽聽

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, –1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, and -324聽are called negative factors of 324.

The list of all the factors of 324, including positive as well as negative numbers, is given below.

Factor list of 324:聽1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 18, -18, 27, -27, 36, -36, 54, -54, 81, -81, 108, -108, 162, -162, 324, and -324

Factors of 324 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 324 are there?

Solution

The total number of Factors of 324 is 15.

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

Example 2

Find the factors of 324 using prime factorization.

Solution

The prime factorization of 324 is given as:

324 $\div$ 2 = 162聽

162 $\div$ 2 = 81

81 $\div$ 3 = 27聽聽

27 $\div$ 3 = 9

9 $\div$ 3 = 3聽聽

3 $\div$ 3 = 1聽

So the prime factorization of 324 can be written as:

2$^2$ x 3$^4$ = 324