Q. 485.0( 3 Votes )

A five-digit number AABAA is divisible by 33. Write all the numbers of this form.

Answer :

Given: A five-digit number AABAA is divisible by 33.


When the number AABAA is divisible by 33 then its divisible by 3 and 11 because when a number say x is divisible by y, then x is divisible by the factors of y as well.


As AABAA is divisible by 3,we can say that sum of all the digits is a multiple of 3.


Therefore A + A + B + A + A = 0,3,6,9,12…


4A + B = 0,3,6,9,12…


Now as AABAA is divisible by 11,then according to the divisibility rule of 11,the difference of sum of digits of odd places and even places should be divisible by 11.


Therefore, for the number AABAA, we can write the difference of sum of digits of odd places and even places as


(A + B + A)-(A + A) = 0,11,22,…


(2A + B)-(2A) = 0,11,22,..


B = 0(As B is a digit in the number AABAA,it can be only 0)


So, A can be any digit like 3,6,9,…and B = 0.


Hence the numbers in the form of AABAA divisible by 33 are


33033,66066 and 99099.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz on Divisibility TestQuiz on Divisibility TestQuiz on Divisibility Test32 mins
Quiz | Who will Win the Game?Quiz | Who will Win the Game?Quiz | Who will Win the Game?41 mins
Divisible or notDivisible or notDivisible or not41 mins
Mastering Divisibility TestMastering Divisibility TestMastering Divisibility Test42 mins
NCERT | Divisibility TestNCERT | Divisibility TestNCERT | Divisibility Test43 mins
Smart Revision | Complete Chapter QuizSmart Revision | Complete Chapter QuizSmart Revision | Complete Chapter Quiz45 mins
Quiz | Imp. Qs. on Playing With NumbersQuiz | Imp. Qs. on Playing With NumbersQuiz | Imp. Qs. on Playing With Numbers45 mins
On the Number lineOn the Number lineOn the Number line44 mins
Essentials of Rational NumbersEssentials of Rational NumbersEssentials of Rational Numbers45 mins
Missing NumbersMissing NumbersMissing Numbers55 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :