How can you quickly find the factors of a number?
Factors are the numbers that divide into another number without leaving a remainder and can never be bigger than the original number.
To find factors quickly start with the number 1 and ask yourself the question: can 1 be divided into the original number without leaving a remainder. As 1 will go into every integer obviously the answer will be yes every time.
So you could start finding your factors by beginning with the number 2 knowing that your factor list will contain 1 and your original number.
Each time you increment your number keep asking yourself the question: can this number be divided into the original number without leaving a remainder?
When you find a number that does divide without remainder into the original add this number to your factor list AND its quotient .
Keep incrementing your number by 1 and stop once tour number exceeds or is the square root of your original number.
Once you’ve finished you will have a set of numbers that will all divide into your original number without leaving a remainder.
If you only have 1 and your original number in the list then your original number was a prime number . As you can probably tell a prime number is a number that has just two factors: itself and the number 1.
If you have more than 2 numbers in your list your original number is known as a composite number . As you can probably tell a composite number is a number that has more than 2 factors.
Lastly, to find the highest factor of a composite number, other than the number itself, simply look at your list of factors and see what the highest number is besides the original number.
Here is a demonstration of how to obtain the factors from a number and to determine whether that number is prime or composite, and if composite what the highest factor is.
Find Factors Of 40
The process for finding the factors of 40 step by step is as follows:
| Find Factors of 40 |
|---|
| Start by inserting into your factor list both the number 1 and 40. |
| Working factor list contains 1 and 40 |
| Increment the factor by 1: 1 + 1 = 2 |
| Can 2 be divided into 40 without leaving a remainder? |
| Yes! Therefore, add both 2 and the quotient 20 into the factor list. |
| Working factor list contains 1, 2, 20 and 40 |
| Increment the factor by 1: 2 + 1 = 3 |
| Can 3 be divided into 40 without leaving a remainder? |
|
No! 3 divided into
|
| Increment the factor by 1: 3 + 1 = 4 |
| Can 4 be divided into 40 without leaving a remainder? |
| Yes! Therefore, add both 4 and the quotient 10 into the factor list. |
| Working factor list contains 1, 2, 4, 10, 20 and 40 |
| Increment the factor by 1: 4 + 1 = 5 |
| Can 5 be divided into 40 without leaving a remainder? |
| Yes! Therefore, add both 5 and the quotient 8 into the factor list. |
| Working factor list contains 1, 2, 4, 5, 8, 10, 20 and 40 |
| Increment the factor by 1: 5 + 1 = 6 |
| Can 6 be divided into 40 without leaving a remainder? |
|
No! 6 divided into
|
| As you have reached (or are about to eclipse) the square root of 40 you can stop here. |
| You now have all the factors of 40 being 1, 2, 4, 5, 8, 10, 20 and 40. |
| As there are more than 2 factors the number 40 is a composite number. |
| The highest factor other than the original number 40 itself is 20. |
As you can see finding the factors of 40 is not difficult, but can be repetitive. If you can write down both the divisor and quotient as you go you can short circuit the process and stop at the square root of your original number.
Summary
The factors of a number are all the numbers from 1 up to the original number that can be divided into the original number without leaving a remainder. The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.
Numbers that only have 1 and itself as factors are known as prime numbers . Whereas if a number has more than 2 factors it is a composite number .