Question

5. P340124Q is an eight digit number divisible by 72.
Find the maximum value of P?
(1) 3 (2) 4 (3) 5. (4) 6​

Answer 1

Maximum value of P is 5.

Option (3) is correct.

Given:

• An eight digit number P340124Q.
• The number is divisible by 72.

To find:

• Find the maximum value of P?
• (1) 3
• (2) 4
• (3) 5
• (4) 6

Solution:

Concept to be used:

1. Divisibility by 72: A number is divisible by 72, if it is divisible by 8 and 9.
2. Divisibility by 8: If last three digits of a number are divisible by 8, then the number is divisible by 8.
3. Divisibility by 9: If the sum of digits of a number is divisible by 9, then the number is divisible by 9.

Step 1:

Find the value of Q.

The last three digits of the number are 24Q.

Q must be 8, then only the number is divisible by 8.

$\frac{248}{8} = 31$

Thus,

Value of Q is 8.

Step 2:

Find the value of maximum value of P.

Sum of digits of number

$P + 22$

if P+22 is divisible by 9, the P must be 5.

Because

$5 + 22 = 27$

and 27 is divisible by 9.

Thus,

Maximum value of P is 5.

Option (3) is correct.

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