FACTORS & MULTIPLES 

MULTIPLE:

 If a number 'x' divides another number ‘y’ exactly, then we say   that y is a multiple of x.

(or)

If a number multiplied by natural numbers the products we get are called multiples of that number.

EXAMPLE:

Multiples of 2 are: 2, 4, 6, 8, 10, 12, ….

Multiples of 5 are: 5, 10, 15, 20, 25, 30,….

NOTE:

✍   Multiples of a given number are all those numbers which are exactly divisible by the given      

       number.

✍  Every multiple of a number is greater than or equal to that number.

✍ The number of multiples of a given number is infinite.

✍ Every number is a multiple of itself and it is the least multiple of that number.

FACTOR:

If a number x divides another number y exactly, then we say x is a factor of y.

                                                          or

A factor of a number is an exact divisor of that number.

EXAMPLE:

Factors of 2 are: 1, 2

Factors of 10 are: 1, 2, 5, 10 .

NOTE:

✍ Every factor of a number is an exact divisor of that number.

✍ Every factor of a number is less than or equal to that number,

✍ Number of factors of a given number is finite.

✍1 is the least factor of any number.

✍ Greatest factor for any number is the number itself.

PERFECT NUMBER:

A number in which sum of all factors is equal to twice the number is called a perfect number.

EXAMPLE:

 1.  The factors of 6 are: l, 2, 3 and 6

Sum of the factors of 6 = 1 +2 +3 +6 =12 = 2 X 6

We find that the sum of all factors of 6 is twice the number.

So 6 is a perfect number.

2.  All the factors of 28 are 1, 2, 4, 7, 14 and 28

Adding these we have, 1 +2+4+7+14+28=56 =2 X 28

The sum of the factors of 28 is equal to twice the given number.

So the number 28 is a perfect number.

3.  Is '15" a perfect number?

SOLUTION: Factors of 15 are 1, 3, 5 and 15

Sum of the factors of 15 = 1+3+5+15 = 24 not twice of 15

So 15 is not a perfect number.

WORKSHEET PDF GIVEN BELOW