# What are factors in Maths?

What is a factor?

Let’s suppose i asked you to find numbers which can exactly divide number 32 leaving 0 remainder.
There are many numbers like this such as 1, 2, 4, 8, 16 etc. which will divide 32 completely, hence are known as factors of number 32.

Factors – All the exact divisors (which give remainder = 0) of a number, are the factors of that number.

For Example:
Let us consider number 32.
Is number 16 is the factor of 32?

Important points –
1. The number of factors of a number are finite (countable)

2. For any number, the factors are always less than that number (except the same number)
i.e. for 8, the factors are 1,2,4 & 8. Here, all its factors are less than 8 except 8.1 is a factor of every number

3. Every number is a factor of itself
As number 24 is divided by 24 itself hence 24 is the factor of itself

4. If the number is even (number ends with 0,2,4,6,8) then 2 is definitely one of its factors

5. If the number ends with 0 and 5, then 5 is definitely one of its factors

How to find factors of a number?

We find the factors of number through prime factorization method.
In this method, the numbers are written as multiple of prime numbers.

Step 1:
Divide the number by first prime number 2 and continue dividing by 2 until it is fully divisible by the number 2

Step 2:
Then divide by next prime numbers 3,5,7 etc. until we get 0 as a remainder

Step 3:
Rewrite the given number as product of prime numbers

Let us study prime factorization with the help of one example

Find the prime factorization of 228

Step 1:
Check if number is divisible by 2
Here 228 is divisible by 2 and leaves number 114

Step 2:
Check if number 114 is divisible by 2
Yes, it is divisible by 2 and leaves number 57

Step 3:
Check if 57 is divisible by 2 –> NO
Check if 57 is divisible by 3 –> YES
Leaves number 19

Step 4
Check if 19 is divisible by 3 –> NO
Number 19 is prime number and is only divisible by 19, leaving number 1

So 228 can be written as the product of prime factors
Hence 228 ==> 2 * 2 * 3 * 19

PRIME FACTORS
The number 228 = 2 * 2 * 3 * 19 are the product of prime factors.

INDIVIDUAL FACTORS
If you want to know individual factors you can write can do following manipulations
a. first 1 and 228 are definitely the factors of 228
b. we can find other factors by choosing combinations of other prime factors.

Find the prime factorization and factors of 189

Step 1:
Check if number 189 is divisible by 2 –> NO

Step 2:
Check if number 189 is divisible by 3
Yes, it is divisible by 3 and leaves number 63

Step 3:
Again check if 63 is divisible by 3 –> YES
Leaves number 21

Again check if 21 is divisible by 3 –> YES
Leaves number 7

Step 4
Now number 7 is divisible by only 7, leaving number 1

So 189 can be written as the product of prime factors
Hence 189 ==> 3 * 3 * 3 * 7

PRIME FACTORS
The number 189 ==> 3 * 3 * 3 * 7 are the product of prime factors.

INDIVIDUAL FACTORS
If you want to know individual factors you can write can do following manipulations
a. first 1 and 189 are definitely the factors of 189
b. we can find other factors by choosing combinations of other prime factors.

Hence by combining different prime factors we can get the list of individual factors
you can see above that 9, 27, 21, 67 are some of the factors we got by using this simple method

Find the Prime Factorization and Factors of 130

Prime Factors of 130 are

Step 1:
Check if number 130 is divisible by 2 –> YES
It is divisible and leaves number 65

Step 2:
Check if number 65 is divisible by 3 –> NO

Step 3:
Again check if 65 is divisible by 5 –> YES
Leaves number 13

Now 13 is only divisible by 13 to leave number 1

So 130 can be written as the product of prime factors
Hence 130 ==> 2 * 5 * 13

PRIME FACTORS
The number 130 ==> 2 * 5 * 13 are the product of prime factors.

INDIVIDUAL FACTORS
If you want to know individual factors you can write can do following manipulations
a. first 1 and 130 are definitely the factors of 130
b. we can find other factors by choosing combinations of other prime factors.

This way by combining different prime factors you can find a list of individual factors

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