Page 55 - ICSE Math 6

Step 3: The smallest prime number is 2. Encircle it and then cross out all the numbers divisible by 2.

Step 4: The next prime number is 3. Encircle it and then cross out all the numbers divisible by 3.
Step 5: Continue this process till all the numbers are either encircled or crossed out.

All the encircled numbers are prime numbers and all the crossed out numbers, except 1,
are composite numbers.

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

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

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

Example 9: Find the prime numbers between 4 and 65.

Solution: Using the method of Eratosthenes, prime numbers between 4 and 65 are 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61.

EXERCISE 4.1

1. Find all the factors of the following numbers.
(a) 27 (b) 36 (c) 60 (d) 220 (e) 174

2. Check whether:
(a) 2 is a factor of 33 (b) 3 is a factor of 200 (c) 5 is a factor of 445 (d) 7 is a factor 2,401
3. Sort out the prime numbers and the composite numbers from 17, 56, 83, 122, 29 and 99.
4. Find the prime numbers between 10 and 50.

5. Write the following.
(a) First six multiples of 2 (b) First five multiples of 5
(c) First ten multiples of 10 (d) First five multiples of 12
6. Write all the prime numbers between 50 and 100.

7. Write all the even numbers between 40 and 60.
8. Write all the odd numbers less than 20.
9. Express each of the following as the sum of two or more prime numbers.
(a) 15 (b) 13 (c) 37
10. Express each of the following numbers as the sum of two odd prime numbers.
(a) 42 (b) 32 (c) 50

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