211 LearnersLast updated on May 26th, 2025
Factors of 306
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.
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.
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:
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.
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.
Prime Factorization
The breaking down of numbers as prime factors is called prime factorization. The factors of 306 are:
306=2x3x3x17
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.
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)
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
Improper calculation in division
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.
factors of 306 Examples
Problem 1
Find the total number of factors of 306.
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.
Problem 2
Verify if 306 is divisible by 9.
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.
Problem 3
Find the GCF of 306 and 459.
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
FAQs on Factors of 306
1.What is the negative pair of 306?
2.What is the LCM of 306 and 657?
3.What is the square root of 306?
4.What number is 306 divisible by?
5.What is the LCM of 144 and 306?
6.How can children in Australia use numbers in everyday life to understand Factors of 306?
7.What are some fun ways kids in Australia can practice Factors of 306 with numbers?
8.What role do numbers and Factors of 306 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 306 skills?
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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