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how many three digit number are divisible by 11?

 First three-digit number that is divisible by 11 = 110

Next number = 110 + 11 = 121

Therefore, 110, 121, 132, …

All are three digit numbers which are divisible by 11 and thus, all these are terms of an A.P. having first term as 110 and common difference as 11.

The maximum possible three-digit number is 999. When we divide it by 11, the remainder will be 9. Clearly, 999 − 9 = 990 is the maximum possible three-digit number that is divisible by 11.

The series is as follows.

110, 121, 132, … 990

Let 990 be the nth term of this A.P.

a = 110

d = 11

an = 990

n = ?

an = a + (n − 1) d

990 = 110 + (n − 1) 11

880 = (n − 1) 11

(n − 1) = 80

n = 81

Therefore, 81 three-digit numbers are divisible by 11.

  • 14
View Full Answer

Ap =121,132........990

a=121

d=11

an = 990

an = a + (n-1)d 

121 + (n-1)11 = 990

11(n-1) =990-121 =869

(n-1) = 869/11 = 79

n=79+1 = 80

Therefore, 80 three digit numbers are divisible by 11

 

Thumbs up plz

  • 2

 actually she hasn't included 110 .... in it ...

  • 2

 sorry Ap =110,132........990

a=110

d=11

an = 990

an = a + (n-1)d

110 + (n-1)11 = 990

11(n-1) =990-110 =880

(n-1) = 880/11 = 80

n=80+1 = 81

Therefore, 81 three digit numbers are divisible by 11

n=79+1 = 80

Therefore, 80 three digit numbers are divisible by 11

 

Thumbs up plz

  • -3

 u have written 2 answers dear .... one wrong one incorrect

  • 0

first term (a) = 110

last term (an)= 990

common difference (d)=11

=>  an = a + (n - 1) d

=> 990=110+(n-1)11

=> 990-110=(n-1)11

=> 880/11=n-1

=> 80 + 1 = n

=> 81 = n

ANSWER = Total of  "81"  3 digits terms are there which are divisible by 11.

Hope this helps :D

  • 5

thanks both of u..wish me luck as tomorrow iz my maths exam :)

  • -2

 all the best ..... ;)

  • -1

thanxie...m too nervous yr..:/

  • -2

 be calm ... aur aaram se patience k saath answer krna .... ;)

  • 0

hmm..i hope i will give the answrs patiently ;)

  • -2

 ;)))))))))

  • -1
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