find the number of natural numbers between 101 and 999 which are divisible by 2 and 5
Answers
Answer:
The number of natural numbers between 101 and 999 which are divisible by both 2 and 5 is 89.
Step-by-step explanation:
Since, the number is divisible by both 2 and 5, means it must be divisible by 10.
In the given numbers, first number that is divisible by 10 is 110.
Next number is 110 + 10 = 120.
The last number that is divisible by 10 is 990.
Thus, the progression will be 110, 120, ..., 990.
All the terms are divisible by 10, and thus forms an A.P. having first term as 110 and the common difference as 10.
We know that, nth term = an = a + (n − 1)d
According to the question,
990 = 110 + (n − 1)10
⇒ 990 = 110 + 10n − 10
⇒ 10n = 990 − 100
⇒ 10n = 890
⇒ n = 89
Thus, the number of natural numbers between 101 and 999 which are divisible by both 2 and 5 is 89.
Answer:
Thus Total such no are 890
Step-by-step explanation:
The number divisible by 2 and 5
are divisible by 2*5=10
Thus the numbers divisible by 10 between are:
110,120,130,............................990
This is an AP with a=110,d=10 and An=990
An=a+(n-1)*d
990=110+(n-1)*10
880=(n-1)10
n-1=88
n=89
Thus Total such no are 890