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When you multiply a prime and a composite number do you always get a composite number?
Product of a prime number and a composite number results in a composite number.Now consider the product of a composite number(a) and a prime number(b) is equal to c.i.e. c = a x bIt is clear that c is divisible by both a and b.Also c is divisible by itself and 1, this means that c has more than two factors.A number having more than two factors is composite, therefore product of a prime number and a composite number results in a composite number.
Is two the first prime number?
yes b/c 1 is neither prime or composite
What composite number can be expressed as product of its factors?
None.A composite number c must have a prime factor psuch that 1 < p < c.Therefore the product of c's factors must be at least p*c which must be greater than c.
If a number has an odd number of factors is it a perfect square?
If you mean 'prime' factors, then an odd number of them CAN'T produce a perfect square. Consider 3 factors ... A, B, and C. If their product were a perfect square, then AxB=C, which can't be true if C is a prime number. For non-prime factors, an odd number of them may or may not be a perfect square: Three factors = not a square: 2 x 3 x 5 = 30. Three factors = a square: 2 x 3 x 6 = 36.
Is 10ac a prime or composite?
Assuming that a and c are both integers, 10ac must be composite because it is equal to 2*5*a*c.
