How can you quickly find the factors of a number?
Factors are the numbers that divide into another number without leaving a remainder.
Factors can never be bigger than the original number. To find all the factors of a number quickly start from 1 and ask yourself if the original number can be divided into this number without leaving a remainder.
As 1 will go into every integer you could start at the number 2 knowing that your factor list will contain 1 and your original number.
As you increment by 1 when you hit or cross over the square root of the original number you can stop.
Here is this process in a step by step guide for finding the factors of 29:
- Start by inserting into your factor list both the number 1 and 29.
- Increment the factor by 1, which should now be 2.
- Ask the question: can 2 be divided into 29 without leaving a remainder?
- No! 2 divided into 29 leaves a remainder of 1.
- Increment the factor by 1, which should now be 3.
- Ask the question: can 3 be divided into 29 without leaving a remainder?
- No! 3 divided into 29 leaves a remainder of 2.
- Increment the factor by 1, which should now be 4.
- Ask the question: can 4 be divided into 29 without leaving a remainder?
- No! 4 divided into 29 leaves a remainder of 1.
- Increment the factor by 1, which should now be 5.
- Ask the question: can 5 be divided into 29 without leaving a remainder?
- No! 5 divided into 29 leaves a remainder of 4.
- As you have reached (or are about to eclipse) the square root of 29 you can stop here.
- As the only factors of 29 are 1 and itself, 29 is known as a prime number .
As you can see finding the factors of 29 is not difficult, but is repetitive. The more you do this process the quicker you will become.
Summary
The factors of a number are all numbers from 1 and up that divide into the original number without leaving a remainder. The factors of 29 are (1, 29).
Numbers that only have 1 and itself as factors are known as prime numbers .
