Question

If $ A679B $ is a $ 5 $ digit number is divisible by $ 72 $ find ‘A’ and ‘B’?

Answer 1

Hint: Here we will first find the factors of the given number and will use the divisibility test for the given five digit number to find the unknown digits “A” and “B”.

Complete step-by-step answer:
First split the given number $ 72 $ into its factors- $ 72 = 8 \times 9 $ ..... (a)
Also, given that $ A679B $ is a $ 5 $ digit number is divisible by $ 72 $
So, obviously it is divisible by
In which divisibility rule of $ 8 $ states that the last three digits of the number should be divisible by $ 8. $
 $ \Rightarrow 79B $ must be divisible by $ 8 $
Only $ B = 2 $ satisfies the above equation. ..... (b)
Now, using the divisibility test as the given number is also divisible by
(By using the equation “a”)
The divisibility rule of $ 9 $ states that the sum of all the digits in the number should be divisible by $ 9. $
Therefore, placing the value from the equation (b) in the given number which gives $ A6792 $
Sum of digits divisible by $ 9 $
 $ \therefore A + 6 + 7 + 9 + 2 = 9a $
Simplify the above equation –
 $ \therefore A + 24 = 9a $ .... (c)
By using trial and hit method-
By trying the multiples of
Place the values in the equation (c)
 $ \Rightarrow A + 24 = 27 $
Make the required term the subject-
 $
   \Rightarrow A = 27 - 24 \\
   \Rightarrow A = 3 \;
  $
Hence, the required answer the values are $ A = 3\,{\text{and B = 2}} $
So, the correct answer is “ $ A = 3\,{\text{and B = 2}} $ ”.

Note: You should be very good in multiples. As, ultimately your answer depends on the multiplication of the numbers. : Multiples are obtained by multiplying the number by the integers. In other words, the multiples of the number are all the numbers that are products of the number and any other natural numbers. For Example – the multiples of $ 2 $ are $ 2,{\text{ 4, 6, 8, 10, 12, 14 , 16}} $ and so on...