Question

Question
Number :
The number of positive integer pin a range 2<n<40 such that tn (n-2)! is not divisible by n is​

Answer 1

Answer:

n−1) is always divisible by n unless and until n is a prime number.

For example,

If we take n=5 then,

5−1=4 which is not divisible 5 as it is a prime number.

and when we take n=6 then,

6−1=5 which is divisible by 6

∴ all prime numbers in the range of 12 to 40 are

13,17,19,23,29,31,37

Hence,the number of positive integer n is 7

Step-by-step explanation:

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Answer 2

Concept:

Factorial is a basic concept in mathematics. Factorials are only products. The factorial is indicated by an exclamation point. The natural numbers that are more than it are multiplied by all the natural numbers that are less than it to get the factor.

The factorial is the multiplication of all positive numbers, let's say "n," that will be less than or equal to n. The letter "n!" stands for a positive integer's factorial.

Given:

2<n<40

Find:

The number of positive integer pin a range 2<n<40 such that tn (n-2)! is not divisible by n is​

Solution:

(n−1)! is always divisible by n unless and until n is a prime number.

For example,

If we take n=5 then,

5−1=4! which is not divisible 5 as it is a prime number.

and when we take n=6 then,

6−1=5! which is divisible by 6

∴ all prime numbers in the range of 2 to 40 are

2,3,5,7,11,13,17,19,23,29,31,37

Hence,the number of positive integer n is 12

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