Determine the smallest counting number that satisfies the following
conditions:
-Divide 7 into this number and you get a remainder of 4.
-Divide 8 into this number and you get a remainder of 5.
-Divide 9 into this number and you get a remainder of 6.
figured out 501
To find the smallest counting number that satisfies these conditions, we will work through each condition one by one.
Condition 1: Divide 7 into this number and you get a remainder of 4.
To find a number that satisfies this condition, we need to find a number that is divisible by 7 and leaves a remainder of 4 when divided by 7. We can start by adding 4 to multiples of 7 until we find the smallest number that satisfies this condition.
7 x 1 = 7 (remainder 0)
7 x 2 = 14 (remainder 0)
7 x 3 = 21 (remainder 0)
7 x 4 = 28 (remainder 0)
7 x 5 = 35 (remainder 0)
7 x 6 = 42 (remainder 0)
7 x 7 = 49 (remainder 0)
...
By incrementing the multiple of 7, we can see that none of them give us a remainder of 4. Therefore, we move on to the next condition.
Condition 2: Divide 8 into this number and you get a remainder of 5.
Similarly, to find a number that satisfies this condition, we need to find a number that is divisible by 8 and leaves a remainder of 5 when divided by 8. We can follow the same approach as before.
8 x 1 = 8 (remainder 0)
8 x 2 = 16 (remainder 0)
8 x 3 = 24 (remainder 0)
8 x 4 = 32 (remainder 0)
8 x 5 = 40 (remainder 0)
8 x 6 = 48 (remainder 0)
8 x 7 = 56 (remainder 0)
...
Once again, by incrementing the multiple of 8, we can see that none of them give us a remainder of 5. Thus, we proceed to the next condition.
Condition 3: Divide 9 into this number and you get a remainder of 6.
We need to find a number that is divisible by 9 and leaves a remainder of 6 when divided by 9.
9 x 1 = 9 (remainder 0)
9 x 2 = 18 (remainder 0)
9 x 3 = 27 (remainder 0)
9 x 4 = 36 (remainder 0)
9 x 5 = 45 (remainder 0)
9 x 6 = 54 (remainder 0)
...
By incrementing the multiple of 9, none of them give us a remainder of 6. Therefore, there is no counting number that satisfies all three conditions.
In summary, there is no smallest counting number that satisfies all the given conditions.