What is the least possible product for digits 1, 3, 5, 6, and 7 using all digits only once?
630
210
To find the least possible product using all the given digits only once, we need to find the lowest possible arrangement of the digits.
One approach to solve this is to order the digits in ascending order and multiply them together. However, since we want the least possible product, we need to consider the position of each digit.
Let's break down the problem step by step:
1. Start by sorting the digits in ascending order: 1, 3, 5, 6, 7.
2. Since we want the least possible product, we should place the lowest digits in the higher place values. So, let's start by placing the digit 1 in the highest place value.
Possible arrangement: 1 _ _ _ _
3. To minimize the product further, we should place the next lowest digit, which is 3, in the next highest place value. This will give us a smaller overall product than placing it in a lower place value.
Possible arrangement: 1 3 _ _ _
4. Continuing with this logic, we place the next lowest digit, which is 5, in the next highest place value.
Possible arrangement: 1 3 5 _ _
5. Next, place the digit 6.
Possible arrangement: 1 3 5 6 _
6. Finally, place the highest digit, which is 7, in the last remaining place value.
Possible arrangement: 1 3 5 6 7
7. Now, multiply all the digits:
1 x 3 x 5 x 6 x 7 = 630
Therefore, the least possible product using all the given digits (1, 3, 5, 6, and 7) only once is 630.