# What is this number? if I divide it by 2, the remainder is 1. If I divide by 3, the remainder is 2.

5 is one number that fits this description, but there are many others as well.

The way to answer a problem like this is to look for a pattern.

You know that if you divide the number by 2, there will be a remainder of 1.  This eliminates half of ALL numbers!!!  2 goes evenly into all even numbers, so your number has to be odd. The number also has to be bigger than 2.

So, start with the list of all odd numbers greater than 2:

3,5,7,9,11,13,15,17,19,21 . . . .

Next, you know that when you divide the number by 3, there is a remainder of 2.  So, any number that is a multiple of 3 (it's in the 3 times table) can't work because there would be no remainder.

get rid of all the multiples of 3 -- I'll put them in bold

3,5,7,9,11,13,15,17,19,21 . . . .

Now test the others to see if you can find a pattern:

Test 5 by dividing it by 3 -- 1 r2 yes

7? 2 r1 no

11? 3 r2 yes

13? 4 r1 no

17? 5 r2 yes

19? 6 r1 no

You can see the pattern.

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5 divided by 2 equals 2 with a remainder of 1.

5 divided by 3 equals 1 with a remainder of 2.

Approved by eNotes Editorial Team