Question

How many of the prime factors of \[30\] are greater than \[2\]?
A. One
B. Two
C. Three
D. Four
E. Five

Answer 1

Hint: In this question, we can use the factorization method. Factorization is a method in which the given number decomposes or breaks into the multiplication of one or many smaller factors such that when we multiply the factors then we are left with the number too. Prime factors are those factors or smaller multiplies that are obtained after the prime factorization of the given number.

Complete step-by-step answer:
Here we have to find out how many prime factors of \[30\] are greater than \[2\].
Firstly we will find the prime factors of \[30\] using the prime factorization method.
In the first step: we have to check that \[30\] is divided by which number or smallest number. Here \[30\] is divisible by \[2\] and we get \[15\] as a remainder and then check Is \[15\] divisible by 2? No therefore check Is \[15\] divisible by \[3\]? Yes, \[15\] is divisible by \[3\] and we left with \[5\], now check for \[5\] .
\[5\] is divisible by \[5\] and we are left with \[5\] so we get \[3\] factors of \[30\] means by which number \[30\] divides completely so the three factors of \[30\] are \[2,3,5\] and according to question, we have to find that how many factors greater than \[2\] are divisible by \[30\]. Factors greater than \[2\] are \[3\] and \[5\].

There are total \[2\] factors of \[30\] greater than \[2\].

Note: Prime factors of prime numbers cannot find out. Prime factors of composite numbers can be calculated only prime numbers and Composite numbers. So, The numbers which get divided by 1 (one ) only, are known as prime numbers. For example 1,2,3,5,7 etc. Those numbers which get divided by other than 1is known as composite numbers Such as \[4,6,8,9\] etc.