How many prime numbers are multiples of 8
The Correct Answer and Explanation is:
Correct Answer:
There are no prime numbers that are multiples of 8.
Explanation:
To understand why, let us explore the definition and properties of prime numbers and multiples:
- What is a Prime Number?
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, 5, 7, and 11. Prime numbers cannot be divided evenly by any other numbers except for 1 and the number itself. - What is a Multiple of 8?
A multiple of 8 is any number that can be expressed as ( 8 \times n ), where ( n ) is a whole number. For example, 8, 16, 24, and 32 are multiples of 8. Importantly, every multiple of 8 is divisible by 8. - Why Can’t a Multiple of 8 Be a Prime Number?
If a number is a multiple of 8, it is divisible by 8. For a number to be prime, it must not have divisors other than 1 and itself. Therefore, any multiple of 8 automatically has at least three divisors: 1, 8, and the number itself. This violates the definition of a prime number. - Examples to Illustrate:
Let’s analyze some multiples of 8:
- ( 8 = 8 \times 1 ) (Divisors: 1, 2, 4, 8 — not prime)
- ( 16 = 8 \times 2 ) (Divisors: 1, 2, 4, 8, 16 — not prime)
- ( 24 = 8 \times 3 ) (Divisors: 1, 2, 3, 4, 6, 8, 12, 24 — not prime)
Since all multiples of 8 have additional divisors, no multiple of 8 can ever be a prime number. Hence, the answer is none.