Answer: an option is 2736
and we only have two possible solutions, the other is 6732
Step-by-step explanation:
we want to write a number:
a73b, where a and b are one digit numbers (0 to 9) in such way that the number is divisible by 36.
Now, we know that 36 is multiple of 6, so 6*6 = 36
The multiples of 36 are always even numbers, so we can discard all the odd options for b.
We also can discard the option a = 0, because we want a 4 digit number.
now, let's do it by brute force.
if a = 1, we have:
173b, now you can give b different values (only even values) and see if some of them is divisible by 36. You will find that none is.
if a = 2
273b
when b = 6, we have:
N = 2736, that is divisible by 36 as:
2736/36 = 79, so this is a multiple of 36.
now, you can keep changing the value of a and find all the different possible solutions.
if a = 3,
373b is not divisible by 36 for any value of b
if a = 4
473b is not divisible by 36 for any value of b
if a = 5
573b is not divisible by 36 for any value of b
if a= 6
673b it is divisible by 36 when b = 2.
6732/36 = 187
if a = 7
773b is not divisible by 36 for any value of b
if a = 8
873b is not divisible by 36 for any value of b
if a = 9
973b is not divisible by 36 for any value of b
So we only have two possible solutions
