Factors of 324

Did you know that 324 is an even composite number obtained as a product of 2s and 3s, two prime numbers? Product of two prime numbers will always result in a composite number, as the two primes which are multiplied will be the factors of that composite number. In this chapter, we will calculate the factors of 324, prime factors of 324, and factors of 324 in pairs along with solved examples for a better understanding.

• Factors of 324: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324
• Prime Factorization of 324: 324 = 2 × 2 × 3 × 3 × 3 × 3 = 2² × 3⁴ 

What Are the Factors of 324?

The numbers which on multiplication give the product as 324 are referred to as factors of 324. The factors of 324 are numbers which divide it without leaving any remainder. So, when we multiply any two whole numbers with each other and get 324 as the answer, we say that both these numbers are the factors of 324.

How to Calculate the Factors of 324?

In order to calculate the factors of 324, we need to find all the numbers which would divide 324 without leaving any remainder. Let's start by checking for the factors of 324, starting from 1 to 324. We can express 324 as a product of its prime factors in the prime factorization method and we divide 324 with its divisors in the division method. For the numbers dividing 324 entirely, the divisors as well as their quotients are the factors of 324.

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

Explore factors using illustrations and interactive examples.

• Factors of 441 - The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441.
• Factors of 108 - The factors of 108 are  1, 2, 3 , 4, 6, 9, 12, 18, 27, 36, 54, and 108.
• Factors of 288 - The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16,18, 24, 32, 36, 48, 72, 96,144, and 288.
• Factors of 81 - The factors of 81 are 1, 3, 9, 27, and 81.
• Factors of 162 - The factors of 162 are 1, 2, 3, 9, 27, 54, 81, and 162.
• Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 324 by Prime Factorization

Prime factorization means expressing a composite number as the product of its prime factors.
To get the prime factorization of 324, we use two methods:

• Method 1: Factor Tree Method
• Method 2: Upside-Down Division Method

Method 1: Factor Tree Method

The factor tree of 324 obtained is:

Method 2: Upside-Down Division Method

We divide 324 by its smallest prime factor, which is 2.

324/2 = 162

Now, 162 is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1. The prime factorization of 324 is shown below:

Hence, the prime factors of 324 are 2 and 3.
The prime factorization of 324 is 2 × 2 × 3 × 3 × 3 × 3.

Factors of 324 in Pairs

The pairs of numbers, which when multiplied give 324, are known as the factor pairs of 324. Observe the following factors of 324 in pairs. If we consider negative integers, then both the numbers in the pair factors will be negative as ( - ve × - ve ) = +ve.

• Positive Pair Factors of 324 are: (1, 324), (2, 162), (3, 108), (4, 81), (6, 54), (9, 36), (12, 27), (18, 18)
• Negative Pair Factors of 324 are: (-1, -324), (-2, -162), (-3, -108), (-4, -81), (-6, -54), (-9, -36), (-12, -27), (-18, -18)

Important Notes:

• As 324 ends with 24 as last two digits and 24 is divisible by 4, 4 is one of the factors of 324.
• 324 is a perfect square number. Thus, one of its pair factors is (18, 18) as 18² is 324.

FAQs on Factors of 324

What are the factors of 324?

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

What are the prime factors of 324?

The prime factors of 324 are 2 and 3.

Are all the factors of 324 prime?

No, all the factors of 324 are not prime.

What are the common factors of 324 and 243?

The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324. The factors of 243 are 1, 3, 9, 27, 81, and 243. Hence, the common factors of 324 and 243 are 1, 3, 9, 27, and 81.

Is 7 a factor of 324?

No, 7 is not a factor of 324.