Page 48 - Start Up Mathematics_6

3 Playing with Numbers

Avinash wants to distribute 12 marbles. He wishes Various Number of Marbles per
to distribute them equally among his friends. ways friend(s) friend
Help him to decide the number of friends and the (a) 1 12
various possibilities of distribution. In the table (b) 2 6
given alongside are all the possible ways in which (c) 3 4
12 marbles can be distributed. We observe that the (d) 4 3
numbers 1, 2, 3, 4, 6 and 12 divide 12 exactly and (e) 6 2
are therefore factors of 12. (f) 12 1

In this chapter, we will study about factors, multiples, test and properties of divisibility, LCM and
HCF of numbers.

Factor

A factor of a number is an exact divisor of that number, i.e., it divides the number completely
without leaving any remainder.

Properties of factors

 1 is a factor of every number.

 Every number is a factor of itself.
 A factor of a number is an exact divisor of that number.

 A factor of a number is either less than or equal to the given number.

 Factors of a number are finite.

Multiple
A multiple of a number is obtained by multiplying it with a natural number. For example, multiples
of 5 are 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15, 5 × 4 = 20, ..., etc.

Properties of multiples

 A multiple of a number is greater than or equal to the number.
 Every number is a multiple of itself.

 Multiples of a number are infinite.

Perfect Number: If the sum of all the factors of a number is equal to twice the number then it is
called a perfect number. An example of perfect number is 6, as the sum of all its factors is twice
6 itself, i.e., 1 + 2 + 3 + 6 = 2 × 6.