Question

The number 36 has the property that it is divisible by the digit in the ones position, because 36 is visible by 6. The number 38 does not have this property. How many numbers between 20 and 30 have this property?

Answer 1

22 is divisible by 2.

Explanation:

And 24 is divisible by 4.
25 is divisible by 5.
30 is divisible by 10, if that counts.
That's about it - three for sure.

Answer 2

The numbers between 20 and 30 inclusive that have the specified property are:

21, 22, 24, and 25

Explanation:

There aren't many numbers between 20 and 30, so it's easy to make a list and test each number to see if it fits this rule.

20 -- cannot divide by zero

21 -- divisible by 1

22 -- divisible by 2

23 -- not divisible by 3 (and it's prime anyway)

24 -- divisible by 4

25 -- divisible by 5

26 -- not divisible by 6

27 -- not divisible by 7
(think "7, 14, 21, 28 ... Oops! Just missed 27.")

28 -- not divisible by 8 ("8, 16, 24, 32 ... Nope. No 28")

29 -- not divisible by 9, and anyway, 29 is prime

30 -- nothing is divisible by 0

Answer:
The numbers between 20 and 30 inclusive that meet the criterion:
21, 22, 24, and 25

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Extra credit:

The general rule is:

• EVERY number that ends in 1 is divisible by 1
• EVERY number that ends in 2 is divisible by 2
• EVERY number that ends in 5 is divisible by 5

Numbers that end in 4 are divisible by 4 IF and ONLY IF the digit that precedes the 4 is an even number.

If the digit that is just before the final 4 is ODD, then the number is not divisible by 4.

In practice, that means that every other number that ends in 4 is divisible by 4.

`24   cancel(34)   44   cancel(54)   64   cancel(74) ...`

`9357color(red)(6)4` is divisible by 4 because the 6 is an even number.

`68872color(red)(5)4` is not evenly divisible by 4 because the 5 is an odd number.