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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

7. Express each of the following as the sum of two odd primes.
(a) 48 (b) 64 (c) 96

8. Express each of the following numbers as the sum of three odd primes:
(a) 27 (b) 41 (c) 63
9. Write the following numbers as sum of twin primes.
(a) 36 (b) 84
10. Take three numbers of 2 digits to check whether the Goldbach conjecture holds true.

11. Take a circle and write numbers 1 to 26 on it in such a way so that the sum and differences of two
consecutive numbers on it is a prime number.

12. Match the Columns:

Column A Column B
(a) 2023 (i) Divisible by 3

(b) 24804 (ii) Divisible by 11
(c) 12892 (iii) Divisible by 8

(d) 6016 (iv) Divisible by 7
13. Check whether the following numbers are prime or composite numbers.

(a) 127 (b) 361 (c) 299 (d) 343
14. Replace * with a suitable digit so that 1756*2 is divisible by 9.

15. ‘The product of three consecutive numbers is always divisible by 6’. Is the statement true? Justify
your answer with examples.

16. Replace * by a digit in the following numbers so that the numbers are divisible by 11.
(a) 92*389 (b) 8*9489

Highest Common Factor (HCF)

We know how to find the common factors of any two or more numbers. Let us now try to find the
highest of these common factors. Factors of 24 Factors of 32

Consider the common factors of 24 and 32. 12

They are 1, 2, 4 and 8. 6 1 16
2
The highest of these common factors is 8. 24 4 32
So, 8 is called the highest common factor (HCF) of 24 and 32. 8
3
The highest common factor (HCF) of two or more given numbers is
the highest (or greatest) of their common factors. It is also known as Common factors of 24 and 32
greatest common divisor (GCD).

Remember
The greatest number that divides two or more given numbers exactly is known as highest common factor
(HCF) or greatest common divisor (GCD).

161 Prime Time