Last updated on May 26th, 2025
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 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.
Factors help us divide numbers equally, making calculations faster and easier. Given below are the methods used to find factors:
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.
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.
The breaking down of numbers as prime factors is called prime factorization. The factors of 306 are:
306=2x3x3x17
A factor tree shows how a number can be parted down into prime factors.306 is broken down into two factors, 2 × 32 × 17.
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)
While learning about factors of 306, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
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.
The number 306 has 12 factors because the formula takes into account all the combinations of the exponents of its prime factors.
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.
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.
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.
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