Answer :

The number 181 is a prime number since it does not have any factors other than 1 and itself.

To determine whether 181 is prime, we need to check if it has any factors other than 1 and itself. We can do this by dividing 181 by all numbers from 2 to its square root (√181), and checking if any of these divisions result in an integer quotient.

Calculating the square root of 181:

√181 ≈ 13.453

Now, let's check for any factors by dividing 181 by numbers up to 13 (excluding 1 and 181):

181 ÷ 2 = 90.5 (not an integer)

181 ÷ 3 = 60.333 (not an integer)

181 ÷ 4 = 45.25 (not an integer)

181 ÷ 5 = 36.2 (not an integer)

181 ÷ 6 = 30.166 (not an integer)

181 ÷ 7 = 25.857 (not an integer)

181 ÷ 8 = 22.625 (not an integer)

181 ÷ 9 = 20.111 (not an integer)

181 ÷ 10 = 18.1 (not an integer)

181 ÷ 11 = 16.455 (not an integer)

181 ÷ 12 = 15.083 (not an integer)

181 ÷ 13 = 13.923 (not an integer)

None of the divisions yield an integer quotient, indicating that 181 is not divisible by any number other than 1 and itself.

Therefore, 181 is a prime number.

The number 181 is a prime number since it does not have any factors other than 1 and itself.

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