Find all possible values of x for which the number 7x3 is divisible by 3. Also, find each such number.

Here, our given number is 7x3, which is divisible by 3.

We know that if number is divisible by 3 only when sum of digits of given number is divisible by 3.

Hence, if 7x3 is divisible by 3, then,

7 + x + 3 = 0, 3, 6, 9,12,…

10 + x = multiple of 3.

Hence, x = (multiple of 3) – 10

Here, possible values for multiples of 3 are 12, 15 and 18

Hence, x = 2, 5 or 8

Hence, possible numbers are 723, 753 and 783

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