Page 40 - Maths Class 06

The pair of prime numbers that differ by 2 are called twin primes.
A prime triplet is a set of three consecutive prime numbers with common difference 2.
e g. ., (3, 5, 7) is the only prime triplet known. 3, 5 and 5, 7 are two pairs of twin primes that have a
common number 5 and the difference between 5 and 3, 7 and 5 is 2.
Two numbers are said to be co-prime when they have NOTE

only 1 as their common factor.
Co-prime numbers are not always
e g. ., Factors of 15 are 1, 3, 5 and 15. prime, e.g., 16.

Factors of 22 are 1, 2, 11 and 22. There are infinite number of pairs of
twin prime numbers.
The only common factor of 15 and 22 is 1. Pair of any primes is always co-prime.
\ 15 and 22 are co-prime numbers.

EX AM PLE 6. The num bers 13 and 31 are prime num bers. Both these num bers have same dig its 1 and 3.
Find such pairs of prime num bers upto 100.
SO LU TION : Such pairs of prime num bers are (17, 71), (37, 73) and (79, 97).
EX AM PLE 7. From the Sieve of Eratosthenes, find five con sec u tive com pos ite num bers.

SO LU TION : The five con sec u tive com pos ite num bers can be 62, 63, 64, 65 and 66.
EX AM PLE 8. Find the great est and small est prime num ber be tween 30 and 60.
SO LU TION : The great est and small est prime num ber be tween 30 and 60 is 59 and 31 re spec tively.

EX AM PLE 9. Express 71 as a sum of three odd num bers.
SO LU TION : 71 = 19 + 23 + 29

Exercise 3.1

1. Write all factors of the following numbers:
(a) 27 (b) 76 (c) 120
2. Find the common factors of:
(a) 10 and 15 (b) 16 and 20 (c) 21 and 35

(d) 3, 6 and 9 (e) 8, 12 and 20 (f) 45, 60 and 105
3. Give the first four multi ples of each:
(a) 5 (b) 13 (c) 17
4. Find the first three common multiples of:

(a) 6 and 9 (b) 10 and 25 (c) 8 and 12
5. Write all the numbers less than 90 which are common multiples of 5 and 6.
6. Write down the prime numbers between:
(a) 1 and 20 (b) 28 and 44 (c) 90 and 120
7. Express each of the following as a sum of two odd primes:

(a) 30 (b) 64 (c) 98

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