Divisible by 2, 5 and 10

In your book, Maths Mela (Chapter 13, Animal Jumps), Question 11 gives fifteen numbers to sort: 90, 22, 38, 30, 75, 45, 66, 78, 62, 40, 84, 56, 25, 95 and 55. For each one we ask: can it be divided exactly by 2? By 5? By 10?

There are quick tests. A number can be divided exactly by 2 if its ones digit is 0, 2, 4, 6 or 8 (it is even). It can be divided exactly by 5 if its ones digit is 0 or 5. It can be divided exactly by 10 if its ones digit is 0.

Now sort. 90, 30 and 40 end in 0, so they can be divided by 2, by 5 and by 10. 45, 25, 75, 95 and 55 end in 5, so they can be divided by 5 but not by 2 (and not by 10). 22, 66, 38, 78, 62, 84 and 56 are even but do not end in 0 or 5, so they can be divided by 2 but not by 5 (and not by 10). That is 3 + 5 + 7 = 15 numbers, all sorted.

Notice something important: 10 = 2 × 5. So a number that can be divided exactly by 10 can always be divided exactly by 2 and by 5 as well. There is no number that divides by 10 but not by 2, or by 10 but not by 5.