Question

if n is sum of first 13986 prime numbers then n is always divisible by

Answer 1

n is divisible by odd number.

Step-by-step explanation:

Out of 13986 prime numbers, 2 will be the even number and rest 13985 will be odd.

We know that the sum of even numbers will be even and sum of even and odd will be odd

For example, sum of 2, 4, 6, 8 will be 20 which is even.

Sum of 3, 5, 7, 9, 11 will be 35 which is odd (Sum of odd number of odd numbers which are odd, i.e., 5 odd numbers)

Sum of 3, 5, 7, 9, 11, 13 will be 48 which is even (Sum of even number of numbers which are odd, i/e., 6 odd numbers)      

So, sum of 13985(which is an odd number) numbers will be odd and when added to even number 2, it becomes an odd number $\Rightarrow$ n is odd.

$\Rightarrow$ n is never divisible by 2.

Therefore, n is divisible by odd numbers.

Answer 2

n is always divisible by none of these if n is the sum of first 13968 prime numbers

Step-by-step explanation:

n is the sum of first 13968 prime numbers

only 2 is the even prime numbers

Hence 13967 numbers will be odd

Sum of two odd numbers is even

sum of two even numbers is even

sum of odd & even number is odd

Hence sum of 13966 = (2 * 6983) odd numbers would be Even

then if 2 is added then

Sum will be even

now if 13967th odd number is added

then sum will be odd

Hence sum of  first 13968 prime numbers will be odd

hence sum of first 13968 prime numbers is not divisible by 2

Hence not divisible by  4, 6 or 8

Hence none of these is right answer

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