Page 38 - Revised Maths Wisdom Class - 6

3 Prime Time

CHAPTER OUTLINES

● Factors and Multiples ● Types of Numbers ● Prime Factorisation of a Number
● Properties of Factors ● Twin Primes and Co-primes ● Divisibility Test
● Properties of Multiples ● Sieve of Eratosthenes ● Amusement with Numbers

RECALL

● A factor of a number completely divides that number without leaving any remainder.
● 1 is a factor of every numbers.
● Every number is a factor of itself as well as a multiple of itself.
● A factor is always smaller than or equal to its number.
● A multiple of a number is obtained by multiplying it by a natural number.
● A multiple is always greater than or equal to its number.
● Factors are limited but multiples are infinite in number.

Factors and Multiples

Factors
A teacher wants to distribute 12 chocolates. He wishes to distribute them equally among students without breaking
a chocolates into pieces. Think of various properties of distribution!

Various ways Number of student(s) Chocolates per student
(i) 1 12

(ii) 2 6
(iii) 3 4

(iv) 4 3
(v) 6 2

(vi) 12 1

In the given table all the possible ways in which 12 chocolates can be distributed without breaking them into pieces.
We observe that the numbers 1, 2, 3, 4, 6 and 12 divide 12 completly therefore these are the factors of 12.
A factor of a number is a complete divisor of that number. For example, 4 divides 20 completly, therefore 4 is a
factor of 20. Similarly, 3 divides 24 completly therefore 3 is a factor of 24.

Multiples
A number is said to be a multiple of any of its factors. For example, factors of 12 are 1, 2, 3, 4, 6 and 12.