Question

how many 5 digit prime numbers can be formed using digits 12345 if the repetition of digits is not allowed​

Answer 1

Step-by-step explanation:

Total numbers formed using 1, 2, 3, 4, and 5 without repetition is 5! = 120.

But the sum of digits (= 1 + 2 + 3 + 4 + 5 = 15) of any number formed is divisible by 3. It means all 120 numbers formed are divisible by 3.

Prime numbers are numbers which only divisible by 1 and itself.

Answer 2

Given :- how many 5 digit prime numbers can be formed using digits 12345 if the repetition of digits is not allowed ?

Answer :-

before checking the number of digits, let's see sum of all digits .

→ 1 + 2 + 3 + 4 + 5 = 15 = 3 * 5 .

as we know that,

• If sum of digits of a number is divisible by 3, then , the given number also divisible by 3 .
• and, a prime number has only 2 factors 1 and itself .

therefore, we can conclude that,

• Using 1, 2, 3 , 4 and 5 we can't form any prime numbers as sum will always be divisible by 3 .

Hence, 5 digit prime numbers can be formed using digits 12345 is zero.

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