can a prime number be a multiple of any other number except itself? Explain why or why not.
No, a prime number cannot be a multiple of any other number except itself.
To understand why, let's first define what a prime number is. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number cannot be divided evenly by any number other than 1 and itself, without leaving a remainder.
Now, let's consider the definition of a multiple. A multiple of a number is any number that can be divided by that number without leaving a remainder. For example, 6 is a multiple of 3 because 6 divided by 3 equals 2 with no remainder.
If a prime number, let's say 'p', is a multiple of another number, let's say 'm', then it implies that 'p' can be divided by 'm' without leaving a remainder. However, by definition, a prime number has no positive divisors other than 1 and itself. Therefore, 'p' cannot be a multiple of any number 'm' unless 'm' is equal to 'p' itself.
In simpler terms, a prime number is only divisible by 1 and itself. It doesn't have any other factors, so it cannot be a multiple of any other number except itself.
For example, let's take the prime number 7. The only two numbers that can divide evenly into 7 are 1 and 7 itself. Any other number, like 2, 3, 4, 5, or 6, would leave a remainder when divided by 7.
So, to answer your question, a prime number cannot be a multiple of any other number except itself.