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We have 2 + 3 = 5, 3 + 7 = 10, 2 + 13 = 15, 3 + 17 = 20 and 11 + 19 = 30; all sums are divisible by 5.

Thus, required pairs of prime numbers are (2, 3); (3, 7); (2, 13); (3, 17) and (11, 19).

Example 8: The numbers 13 and 31 are
prime numbers. Both these numbers Think and Answer
have same digits 1 and 3. Find more 1. What is the smallest prime number? Is it odd or
such pairs of prime numbers up to even?
100. 2. What is the smallest composite number? Is it odd or even?
3. How many prime numbers are less than 50? List them.
Solution: Required pairs of primes 4. ‘Between any two given numbers, the greater one has always
numbers are: (17, 71); (37, 73) and more number of factors’. Is the statement true? Justify your
(79, 97). answer.

create and solve
You can perform this activity in pairs or in small groups.
Steps:
1. Take an A4 sheet of paper and make a 3 × 3 square. 2. Place numbers 1-9 randomly in nine small squares.
1 7 9

8 3 2

4 6 5

3. Find the product of the numbers row-wise and 4. Now make another square grid on another sheet.
column-wise. Write the product on the right side of Write only answers along the grid and challenge
each row and below each column. your partner to fill in the grid with numbers 1-9
such that the products of numbers in the rows and
1 7 9 63 columns are as given here.

8 3 2 48 63

4 6 5 120 48

32 126 90 120

32 126 90

If your partner challenges you with the following and asks you to use only prime/composite numbers, how will you
work out?
Use only prime numbers. Use only composite numbers.

42 4 240

11 154 9 288

195 12 1080

182 99 70 432 144 1200

(Note: You can repeat a number.)

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