Page 54 - ICSE Math 6

Types of Numbers

Even numbers
Any number which is divisible by 2 is called an even number. Examples of even numbers are
0, 2, 4, 6, 8, etc.

Odd numbers

Numbers which are not divisible by 2 are called odd numbers. Examples of odd numbers are
1, 3, 5, 7, 9, etc.

Prime numbers
The numbers other than 1 having only two factors, 1 and the number itself, are called prime numbers.
Examples of prime numbers are 2, 3, 5, 7, 11, 13, etc.
Maths Info
Composite numbers

The numbers having more than two factors are called composite • The smallest prime number
is 2.
numbers. These numbers have at least one factor other than 1 and • The only even number which
the number itself. Since 4 has more than two factors, i.e., 1, 2 and 4, is also prime is 2.
therefore it is a composite number. Similarly, 6, 8, 9, 10, etc., are also • 1 is neither a prime number
nor a composite number.
composite numbers.
Example 5: What is the sum of: (a) two odd numbers, (b) two even numbers and (c) one odd and
one even number?
Solution: (a) Sum of two odd numbers is an even number.

(b) Sum of two even numbers is an even number.
(c) Sum of an odd and an even number is an odd number.

Example 6: Write down separately the prime and composite numbers less than 15.
Solution: Prime numbers less than 15 are 2, 3, 5, 7, 11 and 13.
Composite numbers less than 15 are 4, 6, 8, 9, 10, 12 and 14.

Example 7: Express the following as the sum of two or three odd prime numbers.
(a) 44 (b) 72 (c) 15 (d) 61

Solution: (a) 44 = 13 + 31 (b) 72 = 31 + 41 (c) 15 = 3 + 5 + 7 (d) 61 = 13 + 17 + 31
Example 8: Check which of the given numbers are prime and which are composite.
15, 13, 41, 27, 36
Solution: Factors of 15 = 1, 3, 5 and 15 Factors of 13 = 1 and 13 Factors of 41 = 1 and 41

Factors of 27 = 1, 3, 9 and 27 Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 and 36
Thus, 13 and 41 are prime numbers, and 15, 27 and 36 are composite numbers.

Sieve of Eratosthenes
A Greek mathematician Eratosthenes, gave a method to separate prime numbers from natural numbers
from 1 to 100. The steps of this method are given below.

Step 1: Write down all the natural numbers from 1 to 100 in rows of 10.
Step 2: Cross out 1 as it is not a prime number.

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