Question

Write one digit on each side of 73 to make a four digit multiple of 36. How many different solutions does this problem have? NOW OR NEVER PLS HELP

Answer 1

We are given that we have to divide a four digit number with 36 such that the number is completely divisible.

To find: The unit's and thousand's digits of the number _73_.

First of all, we have to look at the divisibility rule of 36.

36 = 4 $\times$ 9

So, for a number to be divisible by 36, the number should be divisible by 4 and 9 both.

Divisibility rule for 4: For a number to be divisible by 4, the last 2 digits of the  number should be divisible by 4.

Divisibility rule for 9: For a number to be divisible by 9, the sum of all the digits should be divisible by 9.

Applying divisibility rule of 4 to find unit's digit:

The ten's digit is 3. Adding unit's digit: 32 and 36 are divisible by 4.

So, unit's digit can be 2 or 6.

Let us have a look at divisibility rule of 9 to find the thousand's place digit.

Now, the number becomes:

_732 or _736

1. Let us have a look at _732:

Sum of digits = 7 + 3 + 2 = 12

We know that 18 is divisible by 9, so the thousand's digit can be 18 -12 = 6.

So, one number can be 6732.

2. Let us have a look at _736:

Sum of digits = 7 + 3 + 6 = 16

We know that 18 is divisible by 9, so the thousand's digit can be 18 - 16 = 2.

So, one number can be 2736.

Hence, two solutions can be possible.

Answer 2

Answer:

2

Step-by-step explanation: