Question

What is the sum of all natural numbers n such that the product of the digits of n (in base 10) is equal to n² −10n−36 ?

A. 12
B. 13
C. 124
D. 2612

Answer 1

To find the sum of all natural numbers n such that the product of the digits of n is equal to n² - 10n - 36, we analyze the expression and consider possible values of n. The sum of all natural numbers n is 13.

Step-by-step explanation:

To find the sum of all natural numbers n such that the product of the digits of n is equal to n² - 10n - 36, we can start by analyzing the expression on the right side of the equation.

By expanding n² - 10n - 36, we get n² - 10n - 36 = n(n - 10) - 36.

The product of the digits of n can be found by multiplying the individual digits of n. We can use this information to find the possible values of n.

After analyzing the expression and considering the possible values of n, we find that the sum of all natural numbers n is equal to 13. Therefore, the correct answer is option B. 13.