Page 158 - New Medley 5 Semester 1

2. Even × even = even, even × odd = even, odd × even = even and odd × odd
= odd

Note: Any large number ending with the digits 1, 3, 5, 7 or 9 is an odd
number and ending with 0, 2, 4, 6 or 8 is an even number.

Z Z Prime and composite numbers

Consider the following products:

1 × 2 = 2, 1 × 3 = 3, 1 × 5 = 5, 1 × 7 = 7, 1 × 11 = 11, 1 × 13 = 13, etc.

All the numbers 2, 3, 5, 7, 11, 13,... have only two factors 1 and the

number itself. Hence, these are prime numbers. Thus, we can say, a
number divisible by only two numbers 1 and the number itself is called

the prime number.

Now, consider the factors of the numbers like 4, 6, 8, 9, 10, etc. 4
has 1, 2 and 4 as its factors. 6 has 1, 2, 3 and 6 as its factors. Such

numbers are called composite numbers. Thus, we can say, a number

having more than two factors are called composite numbers.

Let us find the primes between the numbers 1 and 100.

Z Z Leave 1 as it is neither prime 1 2 3 4 5 6 7 8 9 10

nor composite.
11 12 13 14 15 16 17 18 19 20
Z Z Circle 2 and cross out all
the multiples of 2. 21 22 23 24 25 26 27 28 29 30

Z Z Circle 3 and cross out all 31 32 33 34 35 36 37 38 39 40
other multiples of 3.
41 42 43 44 45 46 47 48 49 50
Z Z Circle the next uncrossed
51 52 53 54 55 56 57 58 59 60
number, i.e., 5 and cross out
all the multiples of 5. 61 62 63 64 65 66 67 68 69 70

Z Z Circle the next uncrossed
71 72 73 74 75 76 77 78 79 80
number, i.e., 7 and cross the

remaining multiples of 7. 81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

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