Properties of numbers

1.which of following is a perfect number.

A.2                  B.28

C.12                D.19

2.How many prime numbers are exist between 50 and 100.

A.5                 B.8

C.10               D.15

3.Which of following is an even prime number.

A.2                B.4

C.5                D.3

4.Which of following is a composite number.

A.2              B.3

C.4              D.5

ans:-B,C,A,C.

Properties of numbers

Composite number:-A natural number which has more than two factors is called a composite number Ex-4-factors(1,2,4),6-factors(1,2,3,6).
Note:-
1.First composite number is 4.
2.1 is neither composite nor prime number.

Properties of number

Prime numbers:-A natural number which has exactly two factors(1 and itself) is called a prime number Ex:-2-factors(1,2),
3-factors(1,3),19-factors(1,19).
Note:-1.There are 15 prime numbers between 1 and 50.
2.There are 10 prime numbers between 50 and 100.
3.There are 25 prime numbers between 1 and 100.
4.There are 46 prime numbers between 1 and 200.
5.First prime number is 2.
6.Only 2 is an even prime number.

Properties of number

Twin prime numbers-A pair of prime numbers is such that they are differ by 2(difference is 2) is called twin prime numbers.Ex-(3,5),(11,13),(29,31),(41,43),

etc.

1.Which of followings are twin prime numbers.

A.(43,45)         B.(71,73)

C.(7,9)              D.(2,3)

Properties of numbers

Perfect numbers-A natural number whose sum of factors is equal to two times of itself is called a perfect number.ex-factors of 6 is 1,2,3,6. Sum of factors=1+2+3+6=12.

6×2=12,so 6 is a perfect number.

Factors of 28 is 1,2,4,7,14,28.

Sum of factors=1+2+4+7+14+28=56.

28×2=56,so 28 is a perfect number.


Co-prime numbers:-A pair of two numbers a and b are such that HCF(a,b)=1,then a and b are called co-prime numbers.
Ex-(2,3),(5,7),(7,9),(11,17),(10,17).

Properties of Co-prime numbers-

1.          LCM(a,b)=a×b.

  Ex- LCM(4,5)=4×5=20.

         LCM(11,15)=11×15=165.

          LCM(21,29)=21×29=609.

2.          HCF(a,b)=1


      Ex-       HCF(12,17)=1

3.Divisibility-If we take a number 15.

      Here,15=3×5, HCF(3,5)=1,so we say that         3 and 5 are Co-prime numbers to each-        other.
Divisubility of 15- A number which is divisible by 3 and 5 both ,then they will be divisible by 15.

4.Solving question of LCM and HCF-

(1)LCM of two numbers is 24 and HCF is 2,then how many pairs of number are possible?
  Sol-numbers-2x,2y

   LCM=2xy

      a/q  2xy=24

               xy=12=1×12=3×4=2×6

          Here,(2,6) is not a Co-Prime pairs,so                number of pairs is 2.