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11. In the given diagram, write some numbers in each circle. Highlight the numbers that lie in both
circles.

(a) (b)

Even numbers Multiples of 15 Multiples of 8 Multiples of 12
12. Anshu and his friends play the chole-bhature game with two numbers, which are both smaller than
10. The first time anybody says — chole-bhature is after the number 50. What could the numbers be
which are assigned ‘chole’ and ‘bhature’.
Prime and Composite Numbers

Rakesh bought one dozen apples. Nitya and Mithi started arranging them as follows. The
rectangular arrangements of 12 are arranged in columns. 6 apples in 2 columns, 4 apples in 3
columns, 3 apples in 4 columns, 2 apples in 6 columns, 1 apple in 12 columns.

6 × 2 = 12

4 × 3 = 12

3 × 4 = 12

2 × 6 = 12 12 × 1 = 12

Here, the numbers of rows or columns are factors of 12. That is, 1, 2, 3, 4, 6 and 12 are six factors
of 12. A number which has more than two factors is called composite number. Therefore, 12 is a
composite number. Some more such numbers are 4, 6, 8, 9, 10, 14, etc.
Rakesh ate 1 apple and gave 2 each to Nitya and Mithi. The remaining 7 apples are again arranged.
There is only one row of 7 apples or 1 apple in 7 columns.

7 × 1 = 7
12 apples can be arranged in different ways but 7 apples can be arranged in only 1 way. Here,
the number 7 has only two factors 1 and 7. A number which has only two factors is called prime
number. The first 10 prime numbers are – 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

How to Find Prime Numbers?

There is a very simple method to find the prime numbers between any two given numbers. The
method is very simple and known as Sieve method given by Greek mathematician Eratosthenes.

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