Question

401 Find the largest number that you need to test as a divisor to determine whether each of the following is a prime number . ​

Answer 1

Answer:

Probably 20

Nearest perfect square to 401 is 400, whose square root is 20.

So, divide by numbers up to 20 to check whether it is prime or not.

Answer 2

Answer:

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401 is a prime number

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The prime number are 2,3,5,7,11,13,17,19,etc

Let us test divisibility of 401 by these number

• 401 isn't divisible by 2 , because it is not an even number
• 401 isn't divisible by 3, 4+0+1=5 is not divisible by 3.
• 401 isn't divisible by 5 as the last digit is not 0 or 5
• 401 is not divisible by 7 as 401÷7=57, leaving remainder 1.
• 401 is not divisible by 11 as 401÷11=36 leaving remainder 5.
• 401 isn't divisible by 13 as 401 ÷13=30, leaving remainder 11
• 401 is not divisible by 17 as 401/17=23, leaving remainder 10
• 401 isn't divisible by 19 ,as 401÷19=21, leaving remainder 3.
• The next prime numbers is 23 which is greater than the last quotient 21 ,

Thus, the greatest prime number required to test whether 401 is prime or not is 19 . Since 401 is not divisible by 19, So it's a prime number.