Question

Which of the following numbers are prime?
(a) $$23$$
(b) $$51$$
(c) $$37$$
(d) $$26$$.

Answer 1

(a)
$$23$$,
$$23=1\times 23$$,
$$23=23\times 1$$
$$23$$ has only two factors, $$1$$ and $$23$$. Therefore, it is a prime number.
(b) $$51$$,
$$51=1\times 51$$,
$$51=3\times 17$$
$$51$$ has four factors, $$1, 3, 17, 51$$. Therefore, it is not a prime number. It is a composite number.
(c) $$37$$
It has only two factors, $$1$$ and $$37$$. Therefore, it is a prime number.
(d) $$26$$
$$26$$ has four factors $$(1, 2, 13, 26)$$. Therefore, it is not a prime number. It is a composite number.