Question

P is a prime number greater than \[5\] what is the remainder when P is divided by $6$
A $5$
B $1$
C $1$ or $5$
D None of these

Answer 1

Hint: Prime number is the number which has only two factors that is one and themselves. For example, the first five prime numbers are $2,3,5,7,11,13,17,19,21..........$ So for this divide one by one all the prime numbers greater than $5$ and check the remainder .

Complete step-by-step answer:
In this question it is given that the P is a prime number greater than $5$ what is the remainder when P is divided by $6$ ,
So we know that the Prime numbers are numbers that have only two factors that is one and themselves. For example, the first five prime numbers are $2,3,5,7,11,13,17,19,21..........$ .
In the question it is given that prime number is greater than $5$ hence the prime numbers greater than $5$ are , $7,11,13,17,19,21......$
If we divide the $7$ by $6$ we get remainder equal to $1$ .
If we divide the $11$ by $6$ we get remainder is equal to $5$
If we divide the $13$ by $6$ we get remainder equal to $1$ .
If we divide the $17$ by $6$ we get remainder is equal to $5$
Similarly so on
So if we divide any prime number greater than $5$ we only get $1$ or $5$
Hence the Option C is the correct answer .

Note: Those numbers which have more than two factors are called composite numbers .Prime factors are factors of a number that are, themselves, prime numbers.
A factor is numbers that divides a given number without leaving a remainder mean it give integer quantity