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Last updated on May 26th, 2025

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Factors of 306

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Factors are the numbers that divide another number equally, without leaving any remainder. When you multiply two numbers to find another number, the two which are multiplied are factors. You can think of factors as the building blocks that will help you make numbers.

Factors of 306 for Australian Students
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What are the factors of 306?


Factors are the numbers that help us divide things equally without any leftovers. The numbers 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306 are the factors of 306. The number has both positive and negative integers that divide 306 without leaving any remainder. 
 

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How to find the factors of 306?

Factors help us divide numbers equally, making calculations faster and easier. Given below are the methods used to find factors: 
 

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Finding Factors Using Multiplication

In this method, we take two numbers and find the product of those two numbers to get the required number.


Example: 


1×306=306 


 2×153=306 


 2×102=306 


6×51=306 


9×34=306


17×18=306


This means that 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306 are the factors of 306.

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Finding Factors by Division Method

We divide 306 by numbers starting from 1 and see which number gives the remainder of 0.


306 ÷1=306


306÷ 2=153


306÷ 3=102


306÷ 6=51


306 ÷9=34


306 ÷17=18


So the factors are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306.

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Prime Factorization

The breaking down of numbers as prime factors is called prime factorization. The factors of 306 are:
306=2x3x3x17
 

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Factor tree

A factor tree shows how a number can be parted down into prime factors.306 is broken down into two factors, 2 × 32 × 17.

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Factor Pairs

Positive and negative pairs:


The factors of a number will have both the positive and negative numbers:


Positive :(1,2,3,6,9,17,18,34,51,102,153,306)


Negative:(−1,−2,−3,−6,−9,−17,−18,−34,−51,−102,−153,−306)

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Common Mistakes and How to Avoid Them in Factors of 306

While learning about factors of 306, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
 

Mistake 1

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 Improper calculation in division
 

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Children may get confused while performing divisions in the carry forward of numbers, which may lead to improper results. To avoid this, students should practice division to be better at the calculations.
      

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factors of 306 Examples

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Problem 1

Find the total number of factors of 306.

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Prime factorization: 306=21×32×17


Using the formula for total factors:


Total factors=(1+1)(2+1)(1+1)=2×3×2=12.
 

Explanation

The number 306 has 12 factors because the formula takes into account all the combinations of the exponents of its prime factors.
 

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Problem 2

Verify if 306 is divisible by 9.

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The sum of digits: 3+0+6=9


Since 9 is divisible by 9, 306 is divisible by 9.


306÷9=34


Answer: Yes, 306 is divisible by 9.
 

Explanation

Since the sum of the digits (9) is divisible by 9, the number 306 is divisible by 9 as well. When we divide, we get an integer quotient (34), confirming divisibility.
 

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Problem 3

Find the GCF of 306 and 459.

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Factors of 306: 1,2,3,6,9,17,18,34,51,102,153,306


Factors of 459: 1,3,9,17,27,51,153,459


Common factors: 1,3,9,17,51,153


GCF = 153.


 

Explanation

The GCF of 306 and 459 is 153 because it is the highest number that can divide both 306 and 459 without leaving a remainder

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FAQs on Factors of 306

1.What is the negative pair of 306?

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2.What is the LCM of 306 and 657?

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3.What is the square root of 306?

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4.What number is 306 divisible by?

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5.What is the LCM of 144 and 306?

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6.How can children in Australia use numbers in everyday life to understand Factors of 306?

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7.What are some fun ways kids in Australia can practice Factors of 306 with numbers?

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8.What role do numbers and Factors of 306 play in helping children in Australia develop problem-solving skills?

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9.How can families in Australia create number-rich environments to improve Factors of 306 skills?

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Important Glossaries for Factors of 306

  • Prime Factorization: It is a method of splitting down a number into its factors. For example:306=2x3x3x17

 

  • Divisibility: A number is said to be divisible by a certain number, when we divide a number it should give a whole number and not a decimal.

 

  • Even number: A number that when divided by 2 gives a whole number.


 

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About BrightChamps in Australia

At BrightChamps, numbers mean more than just digits—they open doors to a world of possibilities! We’re here to help children across Australia grasp essential math skills, focusing today on Factors of 306 with a special emphasis on factors—in a way that’s fun, engaging, and easy to follow. Whether your child is figuring out the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance to buy gadgets, understanding numbers builds everyday confidence. Our hands-on lessons make learning enjoyable and straightforward. Since kids in Australia learn differently, we customize lessons to suit each child’s style. From Sydney’s vibrant streets to the beautiful Gold Coast beaches, BrightChamps brings math to life throughout Australia. Let’s make factors an exciting part of every child’s math journey!
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