Question

Write one digit on each side of 10 to make a four digit multiple of 72. How many different solutions does this problem have?

Answer 1

Answer:

One solution , x = 4104

Step-by-step explanation:

It is based on divisibility laws .

If number is divisible by 72 then it must be divisible by 8 and 9 . (72 = 8 × 9 )

In other words it should follow divisibility laws of 8 and 9 .

For divisibility by 8

Last three digits must be divided by 8 .

So what should be last digit . from 100, 101 , 102 , 103 ,104 ,105 , 106 , 107 , 108 and 109 only

104 is divisible by 9.

So first digit will be 4.

For divisibility by 9

Sum of digits divisible 9

number is . x104 . So x+1+0+4 = x + 5 is divisible by 9 which is possible if x = 4