Perhaps rather strangely, there is not a simple standard definition of "number".
In the third century BC, Euclid took "number" to mean one of $2,3,4,5,\ldots$, a sequence starting with $2$ and closed under the operation of adding a unit, i.e. if $n$ is a number, then so is $n+1$, so the sequence continues infinitely. Euclid did not consider the "unit" to be a number. That is consistent at least with the meaning of the expression "A number of students asked this question." One wouldn't say that if just one student had done so.
Euclid proved a number of propositions about numbers, including things about divisibility. He introduced what is now the oldest algorithm still in standard use, his algorithm for finding the largest divisor that two numbers share in common. He proved that the list of prime numbers keeps going no matter how far it is extended. (His proof was that if $S$ is any set of prime numbers then $1+\prod S$ has at least one prime factor other than the prime numbers that are in $S$. In fact every prime factor of that number fails to be in $S$.)
Today "numbers" are taken to include $0$ and $1$ and negative integers $-1,-2,-3,\ldots$ and rational numbers, e.g. $10/7$, that result from dividing one integer by another, and "real" numbers that are not rational. "Real" numbers are identified with points on what you may have heard called the "number line". (In a sense Euclid dealt with irrational numbers and in another sense he didn't. He showed that no pair of what he called "numbers" had the same ratio as the ratio of the length of the diagonal of a square to the length of the side. But he didn't consider such ratios to be "numbers".
("$\alpha\rho\iota\theta\mu\omicron\sigma$" is the Greek word used by Euclid, usually (or always?) translated as "number".))
Conventionally "numbers" are taken to include "imaginary" numbers and "complex" numbers. A complex number is a sum of a real number and an imaginary number.
The concept of "number" is sometimes taken to include cardinal numbers of infinite sets, and sometimes taken to include "nonstandard" real numbers, some of which are infinitely large or infinitely small. Occasionally, someone considers quaternions to be "numbers", and that's really only a question of how words should be conventionally used.