Question

Q 3. Solve . (12)

a) Write the definition of prime number.

b) Write all multiples of 4 between 30 and 60 .

c) Which of the following are co prime numbers. i) 9 ,16 ii) 48 ,52

d) Find the common factors of 36,60 .Then find their HCF.

e) Write the definition of twin primes.

f) Write the definition of co prime numbers.

g) Find the value of the 70% of rs 300.

h) What per cent of 240m is 30m

i) Find 90% 0f rs 2700.

j) Convert 12% into fraction in the lowest form.

k) Check whether 15 is a factor of 315 ?

l) List 6 consecutive composite numbers less than 100.​

Answer 1

Step-by-step explanation:

The number that can be divided exactly by itself and 1 for example 7 ,17 and 41

Answer 2

a) Prime number:- those numbers which are only divisible by 1 and itself.

b) All the multiples of 4 between 30 and 60 are:-

⇒ 4 x 8 = 32

⇒ 4 x 9 = 36

⇒ 4 x 10 = 40

⇒ 4 x 11 = 44

⇒ 4 x 12 = 48

⇒ 4 x 13 = 52

⇒ 4 x 14 = 56

c) 48, 52 are co-prime numbers.

• Co-prime numbers:- those numbers which have only one factor is common.

d) Prime factorization of 36 = 2 × 2 × 3 × 3

Prime factorization of 60 = 2 × 2 × 3 × 5

The common factors of 36, 60 are = 2 x 2 x 3.

HCF(36,60) = 12.

e) Twin primes:- a pair of prime numbers whose difference is 2 are known as twin primes numbers.

f) Co prime numbers:- Those numbers in which only one factor is common. Eg.- 42,52.

g) 70% of 300

= (70×300) / 100

= 210

h) Let the unknown percentage be x.

⇒ x% / 100% = 30/240

⇒ x = 12.5%

i) 90% of Rs.2700,

= 2700 × 100/90

= 3000

j) 12/100

The greatest common factor of 12 and 100 is 4, so divide the numerator and denominator by 4:-

= 12 ÷ 4/100 ÷ 4

= 3/25

So, 3/25 is the lowest fraction form of 12%.

k) 315/15 = 21

If we will divide the number 315 by 15, then it would be completely divisible and the quotient would be 21, so we can say that 15 is a factor of 315.

l) Prime numbers between 1 to 100:-

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Between 89 and 97, there are possibly 2 prime numbers with atleast a difference of 8.

So, the first six consecutive composite numbers less than 100 are 90, 91, 92, 93, 94 and 95.