Question

Using the digits 4, 5, 6, 7, 8, each once, construct a 5-digit number which is divisible by 132.

Answer 1

The given digits are 4, 5, 6, 7 and 8.

Here, 132 = 11 × 12 = 3 × 4 × 11

Since 4 + 5 + 6 + 7 + 8 = 30, the numbers formed by 4, 5, 6, 7 and 8 are divisible by 3.

Now, we need to check for disability by 4 and 11.

A number is divisible by 4 if the number formed by the last two digits is divisible by 4.

A number is divisible by 11 if the difference between the sum of the digits at even places and the sum of the digits at odd places is divisible by 11.

Thus, the possible numbers are 58476, 48576, 57684 and 67584.