# "Use the numbers from 1 to 9 once each to produce the largest product possible from multiplying two numbers together." The answer is 87531 x 9642. How do you get this answer? Given: Digits from 1 to 9.

To do: Find two numbers using the digits once each to produce the largest possible product.

As we know, each of the given digits is less than 10, so the product of all of them should be less than 10*10*10*10*10*10*10*10 *10, which is less than 10^9, meaning it will have at most 9 digits.

Here we have to find two numbers: one should be a five digit number and the second a four digit number.

Let us start the first digit with the highest of all: 9.

We know 9 > 8.

Using next two digits 7 and 6, pairing with 9 and 8 in two ways: like 97 x86 and 96 x 87. Let us check which is larger.

Clearly 96 x87 is larger. Same way using next two digits 5 and 4 placing them in two possible ways with 96 and 87 as next place digits: 965 x874 and 964 x 875, checking which product is larger.

We get 964 x 875, which is larger. Proceeding same way with 3 and 2, 9642 x 8753 is the larger product. Still we have one more digit left which is 1.

It can be placed with 9642 or 8753. Let us check both possibilities.

96421 x 8753 and 9642 x87531. We can see that 9642 x87531 gives the larger product.

Hence the two numbers that can be formed by digits 1 to 9 using once each, and producing the largest product, are 87531 and 9642.

Therefore the answer is 87531 x9642.

Approved by eNotes Editorial Team