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PRIME TRIPLET A set of three consecutive prime numbers. differing by 2, is called a prime triplet. 3. Answer the following questions.
The only prime triplet is (3. 5, 7). a. List the even prime numbers between 1 and 20.
b. List the odd prime numbers between 30 and 50.
CO-PRIMES Two numbers are said to be co-primes if they do not have a common factor other than 1.
c. List the prime numbers between 70 and 100.
d. List the prime numbers between 100 and 150.
EXAMPLE:6 (i) 2. 3 (ii) 3, 4 (iii) 4, 5 (iv) 4, 9 (v) 8, 15 e. List the composite numbers between 50 and 70.

4. Identify which of the following pairs are co-primes and which are twin primes.
REMARK 1 Two prime numbers are always co-primes. a. 5 and 7 b. 11 and 13 c. 15 and 17 d. 41 and 43 e. 49 and 51
REMARK 2 Two co-primes need not be prime numbers. 5. Write seven consecutive composite numbers between two prime numbers from
9, 10 are co-primes, while none of 9 and 10 is a prime number. 6. Express each of the following numbers as the sum of two or more primes.
PERFECT NUMBERS If the sum of all the factors of a number ts two times the number, then the number ts a. 32 b. 56 c. 63 d. 130 e.80
called a perfect number. 7. Write down a number which is a multiple of both the numbers.

a. 7 and 5 b. 11 and 13 c. 3 and 19 d. 2 and 17 e. 23 and 7
EXAMPLE:8 (i) 6 is a perfect number, since the factors of 6 are 1, 2, 3, 6 and 8. Are 23 and 92 co-prime numbers? If not, why?
(1 + 2 + 3 + 6) = (2 × 6). 9. Which of the following numbers has 15 as a factor?
(ii) 28 is a perfect number, since the factors of 28 are 1, 2, 4, 7, 14, 28 and a. 115 b. 225 c. 15,625 d. 51,015 e.16,215.
(1 + 2 + 4 + 7 + 14 + 28) = (2 × 28). 10. Which of the following statements are true?

a. All even numbers, except 2, are composite numbers.
JUST TRY:1 Factors of 15 b. No composite number is an odd number.
JUST TRY:2 Factors of 22 c. The number 2 is the smallest prime number
JUST TRY:3 Let us consider the number 7. The multiples of 7 would be: d. There is no largest prime number.
JUST TRY:4 Consider the number 10. The multiples of 10 would be: e. Every number is either a prime number or a composite number.
JUST TRY:5 2 The factors of 2 f. Two consecutive numbers cannot be prime numbers.
JUST TRY:6 3The factors of 3 g. A number and its successor are always co-prime numbers.
JUST TRY:7 5The factors of 5 h. If two numbers are co-prime numbers, at least one of these must be a prime number.
JUST TRY:8 7The factors of 7 i. The sum of two prime numbers cannot be a prime number.
JUST TRY:9 11The factors of 11 are j. The product of two prime numbers is a prime number.
JUST TRY:10 4 Thefactorsof4are
JUST TRY:11 6 The factors of 6 are DIVISIBILITY TESTS FOR 2, 3, 4, 5, 6, 7, 8, 9, 10 AND 11
JUST TRY:1210 The factors of 10 are
JUST TRY:1314 The factors of 14 are (i) TEST OF DIVISIBILITY BY 2 A number is divisible by 2 if its ones digit is 0, 2, 4, 6 or 8.
JUST TRY:14 28 The factors of 28 are EXAMPLE: 1 Each of the numbers 30, 52, 84. 136, 2108 is divisible by 2.
Twin Primes EXAMPLE: 2 None of the numbers 71, 83, 215, 467, 629 is divisible by 2.
JUST TRY:15 3 and 5
JUST TRY:16 5 and 7 (ii) TEST OF DIVISIBILITY BY 3 A number is divisible by 3 if the sum of its digits is divisible by 3.
JUST TRY:17 11 and 13 EXAMPLE: 3 Consider the number 64275.
Co-Prime Numbers Sum of its digits = (6 + 4 + 2 + 7 + 5) = 24, which is divisible by 3.
JUST TRY: 18 2 and 3 Therefore, 64275 is divisible by 3.
JUST TRY: 19 3 and 4 EXAMPLE :4 Consider the number + 3958+ 3.
JUST TRY: 20 5 and 6 Sum of its digits = (3 9 5 + 8 + 3) = 28, which is not divisible by 3.
JUST TRY: 21 6 and 7 Therefore, 39583 is not divisible by 3.
JUST TRY: 22 8 and 9

(iii) TEST OF DIVISIBILITY BY 4 A number is divisible by 4 if the number formed by its digits in the tens and
PRACTICE EXERCISE 2 .2
ones places is divisible by 4.
EXAMPL E: 5 Consider the number 96852.
1 . Write all the possible factors of the following numbers. The number formed by the tens and ones digits is 52, which is divisible by 4.
a. 35 b.64 c. 120 d. 17 e. 729 Therefore, 96852 is divisible by 4.
2. Write the first five multiples of the following numbers. EXAMPLE: 6 Consider the number 61394.
a. 7 b. 11 c. 13 d. 20 e. 25
The number formed by the tens and ones digits is 94, which is not divtsible by 4.
Therefore, 61394 is not divisible by 4.