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Yes, it is always. Assume temporarily that the product of two prime numbers is not always composite. This implies that that at least one product of prime numbers is also prime. Now, say two different prime numbers p and q, when multiplied, equal r. If r is a Prime number, then r's only positive factors are 1 and r. But 1 is not a prime number. This contradicts that both p and q are prime (because either p or q MUST be 1). Therefore, the product of two prime numbers is always composite.
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Does prime factorization of composite numbers include prime and composite numbers?
No, prime factorizations consist entirely of prime numbers.
What kind of numbers must always use with a prime factorization?
Only composite numbershave prime factorizations. Prime factorizations must consist of only prime numbers.
Is the product always the least common multiple of the numbers?
No, only if the numbers are relatively prime.
What are factor and factoring in math?
Factoring is like taking a number apart. It means to express a number as the product of its factors. Factors are either composite numbers or prime numbers (except that 0 and 1 are neither prime nor composite). Chihuahua1492 :0
Is the LCM of a prime number and a composite number a multiple of the prime number?
Yes, the least common multiple (LCM) of a prime number and a composite number will always be a multiple of the prime number. This is because the LCM is the smallest number that is a multiple of both numbers. Since the prime number is a factor of itself and the LCM is a multiple of both numbers, the LCM will always be a multiple of the prime number.
