Nine.
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They are called the factors.
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Use the idea of place-value, and write the corresponding equation. With the 7 at the beginning, your number is 7xxxxx, so the 7 is worth 700,000; with the seven at the end, it is only worth 7. So, if you call your number "n", your equation would be something like700000 + n = 4(n + 7) Solve this, and you get "n" as a 5-digit number.
The number you are looking for is called the reciprocal (or multiplicative inverse). All that sound very complicated, but the reciprocal of a number n is simply 1/n.
(The assumes that "the number" in the question is not n, although if they are they same number, this is still true.) "If the sum of the digits of the number is divisible by n, then the number itself is divisible by n" is true if n is 3 or if n is 9.