Factors of 324

The numbers that divide 324 evenly are known as factors of 324.

A factor of 324 is a number that divides the number without remainder.

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

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

Prime factors of 324: 2 and 3.

Prime factorization of 324: 2² × 3⁴.

The sum of factors of 324: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 324 = 820

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication

• Finding factors using the division method

• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 324. Identifying the numbers which are multiplied to get the number 324 is the multiplication method.

Step 1: Multiply 324 by 1, 324 × 1 = 324.

Step 2: Check for other numbers that give 324 after multiplying

2 × 162 = 324

3 × 108 = 324

4 × 81 = 324

6 × 54 = 324

9 × 36 = 324

12 × 27 = 324

18 × 18 = 324

Therefore, the positive factor pairs of 324 are: (1, 324), (2, 162), (3, 108), (4, 81), (6, 54), (9, 36), (12, 27), (18, 18). For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 324 by 1, 324 ÷ 1 = 324.

Step 2: Continue dividing 324 by the numbers until the remainder becomes 0.

324 ÷ 1 = 324

324 ÷ 2 = 162

324 ÷ 3 = 108

324 ÷ 4 = 81

324 ÷ 6 = 54

324 ÷ 9 = 36

324 ÷ 12 = 27

324 ÷ 18 = 18

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

The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
   
• Using factor tree

Using Prime Factorization: In this process, prime factors of 324 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

324 ÷ 2 = 162

162 ÷ 2 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of 324 are 2 and 3.

The prime factorization of 324 is: 2² × 3⁴.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 324 is divided by 2 to get 162.

Step 2: Now divide 162 by 2 to get 81.

Step 3: Then divide 81 by 3 to get 27.

Step 4: Divide 27 by 3 to get 9.

Step 5: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 324 is: 2² × 3⁴.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 324: (1, 324), (2, 162), (3, 108), (4, 81), (6, 54), (9, 36), (12, 27), and (18, 18).

Negative factor pairs of 324: (-1, -324), (-2, -162), (-3, -108), (-4, -81), (-6, -54), (-9, -36), (-12, -27), and (-18, -18).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.

• Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 324.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 324 are (1, 324), (2, 162), etc.

• Prime factorization: The process of expressing a number as the product of its prime factors. For instance, 324 is 2² × 3⁴.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the number. For example, to find factors of 324, we look for pairs like (9, 36).