Page 53 - Start Up Mathematics_6

(b) Since square root of 617 lies between 24 and 25.
We check whether 617 is divisible by any of the prime numbers 2, 3, 5, 7, 11, 13,
17, 19 and 23. By trial, we find that 617 is not divisible by any of these prime
numbers. We conclude that 617 is a prime number as no number other than
1 and 617 divides it.
Example 12: Fill in the blanks:
(a) 1 is neither _________ nor ____________.

(b) The smallest prime number is ________.
(c) The smallest composite number is_________.
(d) The smallest even natural number is _________. (NCERT)
Solution: (a) 1 is neither prime nor composite.
(b) The smallest prime number is 2 .
(c) The smallest composite number is 4 .
(d) The smallest even natural number is 2 .

EXERCISE 3.2

1. Write all the prime numbers between 50 and 100.
2. Write all the even numbers between 40 and 60.
3. Write all the odd numbers less than 20.
4. Write all the twin primes between 1 and 100.
5. Write down separately the prime and composite numbers less than 30.

6. Express each of the following as a sum of two or more prime numbers:
(a) 15 (b) 13 (c) 37
7. Express each of the following numbers as the sum of twin primes:
(a) 84 (b) 120 (c) 36
8. Express each of the following numbers as the sum of two odd prime numbers:

(a) 42 (b) 32 (c) 50
9. State whether the following statement is True or False:
(a) Every natural number is either a prime number or a composite number.
(b) 1 is a prime number.
(c) The smallest odd composite number is 9.
(d) The sum of any two prime numbers is always an even number.
(e) The product of any two prime numbers is always an odd number.
(f) All even numbers are composite numbers.
(g) The sum of any two prime numbers cannot be a prime.
(h) For a number greater than 10 to be prime, the possible digits in the units place are 1,
3, 7, and 9.

Tests of Divisibility
The process of knowing whether a given number is exactly divisible by another number without
actually dividing is called test of divisibility. Here we shall study the test of divisibility of numbers
by 2, 3, 4, 5, 6, 8, 9, 10 and 11.

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