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Q: When is the product of two numbers a prime number?

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The product of any two numbers, neither of which is 1, is never a prime number.

The product of two prime numbers is always a composite number, and it never is a prime number.

A composite number is the product of two or more prime numbers.

Discounting the exception where the two numbers are 1 and some prime, products of two numbers will not result in a prime number. That results because that result, whatever it might be, will be divisible by 2, in addition to 1 and itself. And as it's divisible by two it's not a prime. So, no, in general a product of two numbers will not be a prime result. ANS.

The product of two prime numbers can never be another prime number, the numbers that you multiplied are factors of the product. (example, 9 times 5 is 45, 9 and 5 go into 45)

No - because its factors include each of the two prime numbers.

No.

A composite number is the product of two or more prime numbers. A prime number has exactly two factors, 1 and the number itself; a composite number has at least one more factor than the two that a prime number has.

If the second number is a multiple of the prime number, than the LCM is the second number. If the second number is not a multiple of the prime number, then the two numbers are relatively prime, and the LCM is the product of the two numbers.

679 is the product of the largest single-digit prime number and the largest two-digit prime number.

No. 15 is the product of two prime numbers: 3 and 5

There are only two prime numbers that are consecutive numbers, 2 and 3. Their product is 2 x 3 = 6. The first prime numbers are 2, 3, 5, and 7 and the only two consecutive prime numbers whose product is a single digit are 2 and 3. (The next two consecutive prime numbers, 3 and 5, have a two-digit product.)

The product of two prime numbers will be composite.

The greatest two-digit prime number is 97. The lowest two-digit prime number is 11. The product of the two numbers is equal to 1067.

A semiprime or a prime square.

None of them can.

No. 2 is a prime number, and any product of 2 and another prime number will be even.

The multiples of any number cannot be prime numbers because such numbers are the product of at least two numbers. Prime numbers, but definition, cannot be cannot be the product of any numbers except itself and one.

A prime number has exactly two factors, 1 and the number itself. 1 is not a prime number, and the product will be a composite number if any other prime is used as a factor and multiplied by another prime.

No not always because composite numbers can be the product of 2 or more prime factors

There are an infinite amount of such numbers.

If the GCF of two numbers is 1, their LCM will be their product. Such numbers are called relatively prime, or co-prime. Any two prime numbers (like 3 and 5) will be that way, but the numbers don't have to be prime (like 4 and 9).

It is impossible for the product of two prime numbers to be prime. It is impossible for the sum of two prime numbers to be prime as long as one of the numbers isn't 2.

Every composite number ... that is, one that is not a prime ... can be written as the product of two or more prime numbers. The primes themselves are the exceptions. A prime number is the product of only ' 1 ' and itself, and ' 1 ' is not considered a prime number.

If the two numbers have no common prime factors, the LCM will be the product of the numbers.