Question

If \( xyz \) is a three-digit number and the product of its digits is \( 70 \), then find the sum of the digits.

• A. 16
• B. 14
• C. 18
• D. 12

Hint:

When product of digits is given, first prime-factorize the number and check which factors are valid digits (1–9).

Answer 1

The Correct Option is A

Step 1: Factorize the number 70.
\[ 70 = 2 \times 5 \times 7 \] Since \( xyz \) is a three-digit number, each digit must be between 1 and 9.
Step 2: Determine possible digit combinations.
The only way to write 70 as a product of three single-digit numbers is: \[ 2, 5, 7 \] All are valid digits (between 1 and 9).
Step 3: Compute the sum of digits.
\[ 2 + 5 + 7 = 14 \] Thus, the sum of the digits is \( 14 \).