How many five digit prime numbers can be obtained by using all the digits 1 2 3 4 and 5 without repe...........

Math and Mental Ability Number System

How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?

This questions was previously asked in

Complete-Test, Previous year (2020)

Zero

One

Nine

Ten

Sol. Ans.(a).

This looks tough, but is not. A number is prime if it is divisible by none other than 1 and itself.

Now take the digits 1,2,3,4 and 5. Just add them up once. We get 15 as the sum. Recall the rule of divisibility by 3.

“If the sum of the digits of a number is divisible by 3 then number will be divisible by 3”.

So any number formed using these five digits will be divisible by 3. So it cannot be prime. Hence zero.

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