Question

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Answer 1

Answer:

There are 89 numbers of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Step-by-step explanation:

Numbers which are divisible by both 2 and 5 are divisible by 10 also.  

The numbers between 101 and 999 which are divisible 10 are : 110, 120, 130,140 ,......,980, 990.  

These number forms an AP .  

Here, first term , a = 110 , Common Difference, d = 120 -110 = 10  and nth term , an = 990  

Let 'n' be the number of terms.

By using the formula , nth term ,an = a + (n -1)d

990 = 110 + (n - 1) 10

990 - 110 = (n - 1) 10

880 = (n - 1) 10

(n - 1) = 880/ 10

(n - 1) = 88

n = 88 + 1  

n = 89

Hence, there are 89 numbers of natural numbers between 101 and 999 which are divisible by both 2 and 5.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

lcm 2 and 5 = 10

first number divisible by 10 from 101 to 999=110

last =990

trick

(990-110 )+1/10 = 88+1 = 89