Question

Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form four two-digit prime numbers using each number once.

a) Prime numbers
b) Composite numbers
c) Perfect squares
d) Odd numbers

Answer 1

The four two-digit prime numbers that can be formed by using each of the digits 1, 2, 3, 4, 5, 6, 7, and 9 exactly once are 23, 41, 67, and 59.

Step-by-step explanation:

The student's task involves forming four two-digit prime numbers using each of the digits 1, 2, 3, 4, 5, 6, 7, and 9 exactly once. As numbers are composed of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, and prime numbers are those that have only two divisors: 1 and itself, we must find combinations of the given digits that satisfy these criteria. After considering the given digits, here are four valid prime numbers:

• 23
• 41
• 67
• 59

These numbers are prime, as no other whole number other than 1 and the number itself can divide them without leaving a remainder. Moreover, each digit from 1 to 9, excluding 8, which was not in the list provided, has been used exactly once across these numbers.