Q3 of 42 Page 17

Suppose a 3-digit number is divisible by 3. Prove that is divisible by 9.

Given that the is divisible by 3


Now,


the expanded form of


= 111a + 111b + 111c


= 111(a +b +c)


Since is divisible by 3


⇒ a +b +c is divisible by 3


Also, 111 (a +b +c) as 1+1+1 = 3 is also divisible by 3


Hence the number is divisible by 9 as the divisibility test of 9 states the number is divisible by 9 if and only if the sum of the digits is divisible by 9


More from this chapter

All 42 →
1

Without actual division, using divisibility rules, classify the following numbers as divisible by 3, 4, 5, 11.

803, 845, 474, 583, 1067, 350, 657, 684, 2187, 4334, 1905, 2548.

 2

How many numbers from 1001 to 2000 are divisible by 4?

 4

If is divisible by 11, find all possible values of a + b.

 1

Using the numbers from 5 to 13, construct a 3 × 3 magic square. What is the magic sum here? What relation is there between the magic sum and the number in the central cell?