Question

find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both ​

Answer 1

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Sorry for giving the answer late but i tried to explain it in as brief as i could.

The number of natural numbers between 102 and 998 which both are divisible by 2 and 5 both is 89.

Step-by-step explanation:

2 = 2 * 1

5 = 5* 1

therefore LCM (2,5) = 10

therefore all the numbers between 102 and 998 will be divisible by 10.

Therefore the numbers will form an AP with common difference 10.

AP:110,120,.......,990.

A(1) = 110 , A(n) = 990

D = A(2) - A(1) = 120-110 = 10.

D = 10.

We know that

A(n) = A(1) + (n-1)d

990 = 110 + (n-1)10

990-110 = 10n-10

10n = 880+10 = 890

Therefore n = 89.

The number of natural numbers between 102 and 998 which both are divisible by 2 and 5 both is 89.