Question:
A five-digit number AABAA is divisible by 33. Write all the numbers of this form.
Solution:
Given, a number of the form AABAA is divisible by 33. Then, it is also divisible by 3 and
11, as if a number a is divisible by b, then it is also divisible by each factor of b.
Since, AABAA is divisible by 3, sum its digits is also divisible by 3. i.e. 4 + 4 + 8 + A + .4 = 0,3, 6,9…
or 4/4 + 8 = 0, 3, 6 9,… …(i)
From Eq. (i), we have
Further, the given number is also divisible by 11, therefore (2/4 + 8) – 2A = 0,11,22,…
B=Q 11,22,…
8 = 0 [v8 is a digit of the given number]
4/4 = 12or 24 or 36 A= 3, 6 9
Hence, the required numbers are 33033, 66066 and 99099.