BASIC ARITHMETIC (Factors of a certain number)

Although finding the lowest common factors of a number is simple,sometimes knowing the factors of a certain number may be confusing.

If a number can be divided by another number without a remainder, the second number is a factor of the first.

The numbers 1,2,3,4,5,10, and 20 will divide 20. So they are all factors of 20.

Factors of a given number therefore are those numbers,which can divide the given number without a reminder.

To find the factors of a number,start from 1,2,3 .... to get the numbers that can divide the given number without a remainder.

Example: Find the factor of 63.
Solution:
63= 1,3,7,9,21,63

Example: Find the factor of 120.
Solution:
120= 1,2,4,5,6,8,10,12,15,20,24,30,40,60,120

Example: Find the factor of 28.
Solution:
28= 1,2,4,7,14,28

Example: Find the factor of 9.
Hint: Start from one and divide through to nine to know those numbers that can divide nine without remainder that is the factors of nine,You got it!
Solution:
Let's start with one.
9÷1=9 (Therefore one is a factor)
Now let's try two.
9÷2=4.5 (Therefore two is not a factor because there is a remainder )
Let's try with three.
9÷3=3 (Therefore three is a factor)
Let's try with four.
9÷4=2.25 (Therefore four is not a factor because there is a remainder)
Let's try with five.
9÷5=1.8 (Therefore five is not a factor because there is a remainder)
Let's try with six.
9÷6=1.5 (Therefore six is not a factor because there is a remainder)
Let's try with seven.
9÷7=1.2857 (Therefore seven is not a factor because there is a remainder)
Now let's try with eight.
9÷8=1.125 (Therefore eight is not a factor because there is a remainder)
Finally let's try with nine.
9÷9=1 (Therefore nine is a factor)
So therefore the factors are 1,3,9.
Hence factors of 9=1,3,9.
You don't  necessarily  need to show the above working, it is just for your learning purpose.


Example: Write 20 as the product of two factors.
Solution:
Firstly factors of 20 are 1,2,4,5,10,20.
Secondly writing 20 as the product of two factors can be done like this.
20=1×20=2×10=4×5=5×4=10×2=20×1
You have observed that this can be done in six ways.

Take note that one(1) is a factor of all numbers.
Also note that every number is a factor of itself.