Question

For each of the three-digit numbers with no digits zero, the difference between the number itself and the product of its digits is calculated. The largest such difference is

a) 110
b) 270
c) 902
d) 910
e) 927

Answer 1

To find the largest difference between a three-digit number and the product of its digits, list out all the three-digit numbers without zeros, calculate the difference for each number, and find the largest difference.

Step-by-step explanation:

The question asks for the largest difference between a three-digit number and the product of its digits, for numbers that have no zeros in them. Let's break it down step by step.

1. First, we need to list out all the three-digit numbers that have no zeros in them. These numbers range from 123 to 987.
2. Next, we calculate the difference between each number and the product of its digits. For example, for the number 123, the product of its digits is 1 x 2 x 3 = 6. The difference is 123 - 6 = 117. We do this for all the numbers.
3. Finally, we find the largest difference among all the numbers. From our calculations, we find that the largest difference is 927 (for the number 876). Therefore, the correct answer is e) 927.