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.
To find the greatest common factor (GCF) of 42a^2b and 60ab^2, we first need to break down each term into its prime factors. For 42a^2b, the prime factors are 2 * 3 * 7 * a * a * b. For 60ab^2, the prime factors are 2 * 2 * 3 * 5 * a * b * b. Comparing the prime factors of both terms, we can identify the common factors: 2, 3, a, and b. Therefore, the GCF of 42a^2b and 60ab^2 is 6ab.
It is: B 31 is a prime number because it has only two factors which are itself and one
10 is not prime and can't be a prime factor.
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.
Prime factors are factors that are also prime numbers.