How to find All Factors of a Number

Factor of a number is a number that divides it completely, leaving no remainder.

• one-by-one divide given number by 1, 2, 3, ……. until you will start getting repeated numbers. 

 

• STOP there. 

 

• List all those numbers which divides the given number completely, leaving no remainder.

 

• They are all factors of the given number.

 

Let us understand all this procedure by an example.

 

EXAMPLE: Find all factors of 32.

SOLUTION:

32 ÷ 1 = 32

32 ÷ 2 = 16

 

32 ÷ 3 is 10 and 2 remainder. So, ignore it.

 

32 ÷ 4 = 8

 

32 ÷ 5 is 6 and 2 remainder. So, ignore it. 

 

32 ÷ 6 is 5 and 2 remainder. So, ignore it.

 

32 ÷ 7 is 4 and 4 remainder. So, ignore it.

 

32 ÷ 8 = 4

Now the numbers started repeating, 4 and 8. So stop.Thus, all the factors of 32 are: 1, 2, 4, 8, 16, 32(Observe that all factors are in pair. Their product gives 32.1 × 32 = 322 × 16 = 324 × 8 = 32) FACT 1: All factors of ANY number are always finite in number.In above example, 32 has six factors.FACT 2: Every number, excluding 0 and 1, has a minimum of two factors: 1 and the number itself.

FACT 3: Any factor of a number is always less than or equal to that number.

FACT 4:  2 is a factor of all even numbers. 

FACT 5:  5 is a factor for all numbers that end in 0 and 5. 

FACT 6:  All Square Numbers have an odd number of factors. 

Square Number is a number which is a square of any number.

In other words, it is the product of some number with itself. 

1, 4, 9, 16, 25, ………

 

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