Is 473 divisible by 7

Answer 1

There is no easy test for divisibility by 7, it is often just as quick, if not quicker, to do the division than any devised test.

One test I can suggest:

1) split the number into blocks of 3 digits starting from the right hand end (just like when inserting commas to make a number easier to read);

2) Separately sum the units digits, tens digits and hundreds digits of each block by alternately subtracting and adding starting from the right hand end;

3) Add the sum of the units digits to 3 times the sum of the tens digits to twice the sum of the hundreds digits;

4) if the sum in step 4 is divisible by 7, then so is the original number.

got 473: 3 +3×7 + 2×4 = 32 which is not divisible by 7, so 473 is not divisible by 7.