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Do perfect squares have an even or odd set of prime factors?
FactorsPerfect squares have an odd number of factors. If you think of factor pairs, the pair of factor that when multiplied together equals the given number, you realize that there are two factors for each pair until you come to the factor that when squared equals the number. For example, the factor pairs of 16 are 1 x 16, 2 x 8, and 4 x 4, giving us the factors of 1, 2, 4, 8, and 16 - an odd number of factors.Prime FactorsHowever, the situation is different with prime factors. It will depend on whether you list every prime factor or only the distinct prime factors. There will always be an even number of prime factors because when you square a number, you double the prime factors, which means you have an even number. That is not the case for distinct prime factors, because when you square a number, you are not adding any additional distinct factors. So, in some cases, there will be an even number of distinct prime factors and sometimes an odd number. Some examples follow.4 = 2 x 2. There are two prime factors, but one distinct prime factor.36 = 2 x 2 x 3 x 3. There are four prime factors and two distinct prime factors.900 = 2 x 2 x 3 x 3 x 5 x 5. There are six prime factors and three distinct prime factors.
Can two numbers have 20 as HCF and 535 as LCM?
HCF of 20 means the two numbers have common prime factors of 2, 2 and 5. However, LCM of 535 means that both of the numbers are odd. This cannot be the case if they have a prime factor of 2. Thus two numbers cannot have 20 as hcf and 535 as lcm.
What is the whole number greater than 1 with only two factors 1 and itself?
Two.A number with only two factors, one and itself, is called a prime number. The only even whole prime number is two. Your question implies that there is only one whole number greater than one which is prime, however, since odd numbers are whole numbers, and odd numbers (but not even) are prime, there are infinite prime numbers (since no one has checked each number to infinity to see if it's prime, and, obviously, never will, most assume that the list of prime whole numbers is not finite). Examples are 3, 5, and 13. 9 is an example of an odd number which is not prime.
What numbers have just two factors?
Prime numbers have only two factors, 1 and themselves, so only prime numbers could have only two factors
What is it called when a number only has two factors?
A number that has only two factors is called a prime. The only factors of a prime are 1 and the number itself.
