Question

Find the number of natural numbers between 105 and 995 which are divisible by 2 and 5 both.

Answer 1

Answer:

The total number of natural numbers is 89.

Step-by-step explanation:

To find : The number of natural numbers between 102 and 998 which are divisible by 2 and 5 both ?

Solution :

The number divisible by 2 and 5 both is the number which is divisible by 10.

The number of natural numbers between 102 and 998 which are divisible by 2 and 5 both are 110,120,130,.... 990 forming an Arithmetic progression.

Where, First term is a=110

The common difference is d=10

The last term is l=990

The last term formula is given by,

l=a+(n-1)dl=a+(n−1)d

990=110+(n-1)10990=110+(n−1)10

990-110=(n-1)10990−110=(n−1)10

880=(n-1)10880=(n−1)10

\frac{880}{10}=n-110880=n−1

n-1=88n−1=88

n=88+1n=88+1

n=89n=89

The total number of natural numbers is 89.