B, as a variable, can stand for any number. The factor possibilities are infinite.
b. 2x2x5 are prime factors
a and b have no common prime factors. Their LCM is their product.
I wonder if you mean 56a2b2 ? If so you have 2 x 2 x 2 x 7 x a x a x b x b. If a and/or b are not prime, you will have the factors of those as well.
A factor of a integer is an integer that divides the second integer into a third integer exactly; i.e. A is a factor of B if B/A is exactly C, where all of A, B and C are integers. A prime factor is a factor as above, but is also a prime number. This means that the only factors of that factor are one and the number itself; i.e. A is a prime factor of B if B/A is exactly C andthe only factors of A are 1 and A.
Any number of the form a*b^4 where a and b are different prime numbers, or c^9 where c is a prime, will have exactly 10 factors.
A prime number is a number that has only two factors which are itself and one.
Variables can be any number, which leaves an infinite possibility of factors.
It is: B 31 is a prime number because it has only two factors which are itself and one
Proof by contradiction: suppose that root 7 (I'll write sqrt(7)) is a rational number, then we can write sqrt(7)=a/b where a and b are integers in their lowest form (ie they are fully cancelled). Then square both sides, you get 7=(a^2)/(b^2) rearranging gives (a^2)=7(b^2). Now consider the prime factors of a and b. Their squares have an even number of prime factors (eg. every prime factor of a is there twice in a squared). So a^2 and b^2 have an even number of prime factors. But 7(b^2) then has an odd number of prime factors. But a^2 can't have an odd and an even number of prime factors by unique factorisation. Contradiction X So root 7 is irrational.
10 is not prime and can't be a prime factor.
Prime factors are factors that are also prime numbers.
If it's just factors, then any number have an even amount of factors. Let a be any number, a = 1 a so a have two factors, 1 and a. Two is even. But if the question is what number have an even amount of PRIME factors, then it is different. Because if a is not prime, the might exist another two numbers b and c != 1 such that a = b c. and also, b is not prime, b = d e So a = bc = de c = c d e So a have three prime factors (1 is not prime for some reason) Then this question is less trivial: 6 have only prime factor 2 and 3, 10 only have prime factor 2 and 5, they are even. but 9 only have prime factor 3, so it's not an even amount, so 9 is not.