If the number is 4-digit, the least significant digit will not be 0, because that would require the most significant digit to be 0 as well. (4*0=0)

Suitable least-significant/most-significant pairs are

2/8, the number is 8xy2

4/6, the number is 6xy4

6/4, the number is 4xy6

8/2, the number is 2xy8

The most-significant digit will cause a carry into the 5th digit when any of the first 3 of these is multiplied by 4. So, the number must be of the form 2xy8.

We can write equations for x and y assuming n is the number carried over into the next place.

4y+3 = x+10n

4x+n = y (assuming no carry)

4(4x+n) +3 = x+10n (substitute the second equation into the first)

16x + 4n +3 = x + 10n (multiply it out)

15x + 3 = 6n (subtract 4n+x from both sides)

5x + 1 = 2n (divide both sides by 3)

x must be odd, so possible values are 1,3,5,7,9

x=1, n=3

x=3, n=8

Since n is the carry from the second column to the third, we're pretty sure it won't be 8 or higher. Thus, x=1 and y=(4*1+3)=7

Suitable least-significant/most-significant pairs are

2/8, the number is 8xy2

4/6, the number is 6xy4

6/4, the number is 4xy6

8/2, the number is 2xy8

The most-significant digit will cause a carry into the 5th digit when any of the first 3 of these is multiplied by 4. So, the number must be of the form 2xy8.

We can write equations for x and y assuming n is the number carried over into the next place.

4y+3 = x+10n

4x+n = y (assuming no carry)

4(4x+n) +3 = x+10n (substitute the second equation into the first)

16x + 4n +3 = x + 10n (multiply it out)

15x + 3 = 6n (subtract 4n+x from both sides)

5x + 1 = 2n (divide both sides by 3)

x must be odd, so possible values are 1,3,5,7,9

x=1, n=3

x=3, n=8

Since n is the carry from the second column to the third, we're pretty sure it won't be 8 or higher. Thus, x=1 and y=(4*1+3)=7

**The number you seek is 2178.**When multiplied by 4, it is 8712.