I am thinking of a three-digit number. If you subtract 5 from it, the result is divisible by 5. If you subtract 6 from it, the result is divisible by 6 and if you subtract 7 from it, the result is divisible by 7. What is the smallest number that will satisy these conditions?
" If you subtract 5 from it, the result is divisible by 5" ----> number could be 5,10,15,20....
" If you subtract 6 from it, the result is divisible by 6 "
---> number could be 6, 12, 18 , ...
" if you subtract 7 from it, the result is divisible by 7"
---> number could be 7,14
so it must be a multiple of 5,6, and 7
5x6x7 = 210
check:
210 - 5 is divisible by 5
210-6 is divisible by 6
210-7 is divisible by 7
yup! It's 210
To find the smallest three-digit number that satisfies these conditions, we need to find the smallest number that is divisible by each of the given differences (5, 6, and 7).
Let's start by finding the number that is divisible by 5. We know that when we subtract 5 from this number, the result should be divisible by 5. Therefore, the number must end with either 0 or 5. Since we are looking for the smallest number, we start with 5.
Next, let's find the number that is divisible by 6. We subtract 6 from the number we found in the previous step, and the result should be divisible by 6. The smallest three-digit number that satisfies this condition is 96.
Finally, we need to find the number that is divisible by 7. Subtracting 7 from 96 gives us 89, which is not divisible by 7.
To find the smallest number that satisfies all the conditions, we continue incrementing our number by 10 and repeat the previous steps until we find a number that is divisible by 7.
Starting with 5, we can try 15, 25, 35, ..., and so on. When we reach 35, we find that subtracting 5, 6, and 7 from it all result in numbers that are divisible by their respective differences.
Therefore, the smallest three-digit number that satisfies these conditions is 35.
To find the smallest number that satisfies these conditions, we can start by looking for a number that is divisible by 5, 6, and 7.
First, consider the condition that the number subtracted with 5 is divisible by 5. If a number is divisible by 5, its units digit must be either 0 or 5. Therefore, our number should end in either 0 or 5.
Next, consider the condition that the number subtracted with 6 is divisible by 6. For a number to be divisible by 6, it must be divisible by both 2 and 3. Since the units digit must be 0 or 5, this means that the number must be even to be divisible by 2. Therefore, our number should end in 0.
Finally, consider the condition that the number subtracted with 7 is divisible by 7. In order to satisfy this condition, we need to find the smallest number that becomes divisible by 7 when we subtract 7 from a number ending in 0. The smallest positive number that satisfies this condition is 35, which becomes divisible by 7 when we subtract 7 from it.
So, the smallest number that satisfies all the given conditions is 35.