# 5

## Information we Know

We need to find out the next smallest number that is divisible by 5, but leaves a remainder of 1 when divided by 2,3,and 4.

The smallest number that is divisible by 5 that leaves a remainder of 1 when its divided by 2,3,and 4 is...

## Step 1

First we need to look at the next number it can be divided by five which is 30. We can start by 2 and because 30 is an even number it will divide evenly so it will not have a reminder of one.

## Now we Know

We need to find out the next smallest number that is divisible by 5 but leaves a remainder of 1 when divided by 2,3,and 4. Remember that the smallest number is 25.

The smallest number that is divisible by 5 that leaves a remainder of 1 when its divided by 2,3,and 5 is... 25.

The number can not be a even number.

Every odd number will have a remainder of one

## Step 2

35 is the next number we have to look at we could automatically start on 3 because we know that we will get a remainder of 1 when its a odd number. 3x10 is 30 and 3x1 is 3 that makes 33 but there would be a remainder of 2 so we will have to move on

## Step 3

Now we will skip the number 40 and move on to 45 because 40 is an even number. Let's start with 3. 3x10 is 30 and 3x5 is 15 so we could not use this number.

## step 4

Skip 50 lets go to 55, 10x3 is 30 and3x8 is 24 altogether it is 54 so 3 works. Now let's do it with 4,4x10 is 40 and 4x3 is 12 and that is 52 so the remainder of 3. We can not use this number.

## Step 5

now 65, 3x10 is 30, 3x10 is 30 and 3x1 is 3 which is 63. So we would get the remainder of 2.

## Step 6

75, 3x20 is 60 3x5 is 15 is 75 so let's go to the next number.

## Step 7

85, 3x20 is 60 and 3x8 is 24 so it would have a remainder of 1. 4x20 is 80 and 4x1 is 4, 85 works. That means the next number is 85 is the next smallest number