Page 42 - Maths Skill - 6

40 Maths

Example 2: Write first five multiples of:

(i) 15 (ii) 18
Solution: (i) The first five multiples of 15 are: (ii) The first five multiples of 18 are:
15 × 1 = 15 18 × 1 = 18
15 × 2 = 30 18 × 2 = 36
15 × 3 = 45 18 × 3 = 54
15 × 4 = 60 18 × 4 = 72
15 × 5 = 75 18 × 5 = 90
Example 3: Express each of the following numbers as a sum of two odd primes.
(i) 22 (ii) 26
Solution: (i) 22 = 3 + 19 (ii) 26 = 3 + 23
or or
= 5 + 17 = 7 + 19

Activity
Sieve Method of Finding Prime and Composite Numbers

Eratosthenes, a Greek Mathematician gave a very simple method of finding the prime and composite numbers.
The method is known as the Sieve of Eratosthenes.

1. First write the numbers from 1 to 100 as shown below.
2. Cross out 1 as it is neither a prime number nor a composite number.
3. Encircle 2 and cross out all multiples of 2 in the table (i.e., 4, 6, 8, 10, 12, ...).
4. Encircle 3 and cross out all multiples of 3 in the table (i.e., 6, 9, 12, 15, 18, 21, ...).
5. Next encircle 5 and cross out all multiples of 5 in the table (i.e., 5, 10, 15, ...).
6. Continue this process till every number is either encircled or crossed out.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30
All the encircled
31 32 33 34 35 36 37 38 39 40 numbers so obtained are
prime numbers. And all
41 42 43 44 45 46 47 48 49 50 the crossed out numbers
except 1 are composite
51 52 53 54 55 56 57 58 59 60 numbers.

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100