Answer:
Greatest prime is 83 to test 6971 is prime.
Step-by-step explanation:
To find : What is the greatest prime you must consider to test whether 6971 is prime.
Solution :
To determine whether it is prime or not we check it by taking the root and check the nearest prime factor of it
Step 1 - Take the square root of number 6971
[tex]\sqrt{6971}=83.49[/tex]
Step 2- The last prime number before 83.49
Prime number is 83
Step 3 - Write all the prime number till 83 and if none of the digit divide 6971 then 6971 is prime.
So the only factors to check for 6971 are: 2, 3, 5, 7, 11, 13, 17, 19,, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83.
None of them divides the number
Therefore, 6971 is a prime number.
Greatest prime is 83 to test whether it is prime or not.
Prime numbers are numbers that can only be divided by 1 and itself.
The greatest prime number to test whether 6971 is prime is 83
The number is given as:
[tex]\mathbf{n = 6971}[/tex]
Take square roots of both sides
[tex]\mathbf{\sqrt n = \sqrt{6971}}[/tex]
[tex]\mathbf{\sqrt n = 83.49}[/tex]
Remove numbers after decimal point (do not approximate)
[tex]\mathbf{\sqrt n = 83}[/tex]
There are 23 prime numbers between 1 and 83 (inclusive), and none of these prime numbers can divide 6971
This means that: the greatest prime number to test whether 6971 is prime is 83
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