Start with the easy questions.
Is 17875 divisible by 2? No, because 5 is not even.
Is 17875 divisible by 3? No, because 1+7+8+7+5 = 28, which is not divisible by 3.
Is 17875 divisible by 5? Yes, because it ends in a 5 or 0.
17875/5 = 3575
3575/5 = 715
715/5 = 143
143 doesn't end in a 0 or 5, so no more 5's.
143 = 11 * 13
17875 = 5 * 5 * 5 * 11 * 13