Greatest 2 digit multiple of seven is 98 and the greatest two digit prime is 97
You can find whether a number is a prime or not by following this procedure.
1. Take the square root of the number (for nearest possible perfect square preferably (lower one ). Let the square root be n
2. Check if the number is divisible by any of the prime numbers less than n.
If it is then it is not prime.If it is not divisible then it is prime
could you please make an exemple take in account the numeber of my post above.
Greatest two digit prime number
first, all two digit even numbers are not prime .More over we can easily identify a two digit number which is a multiple of three.
1. 99 is not prime(multiple of three)
2.sqrt of 97= 9. some thing.
now take all the prime numbers less than or equal to 9. they are 7 , 5 , 3, 2 .97 is not divisible by 7 or 5 or 3 or 2. So this is why it is a prime.
The explanation how this concept works concept is as follows.
for example take a number say 30 .
We can write it as
You can see that for every pair of factors one number is below the square root and another above the square root. So using this example we can say that if the number has no factors below the square root then it will not be a prime number.
Now why only prime numbers should be considered?Why are we leaving composite numbers?
Again we can understand this by an example.
lets take 70
Its factors are 1,2,5,7,14,35,70
sqrt of 70 = 8. something
consider all the numbers below 8.
consider 6 first .It is not divisible by 6.
now consider 3 .It is not divisible by 3.
If a number is not divisible by 3 itself it is not divisible by any multiple of three.Same with all the even composites.If a number is not divisible by 2 then it is not divisible by any of the even composites.so every composite below the sqrt of the given number will have a prime factor.If the given number is not divisible by the prime factor itself then it is not divisible by the composite.This is the reason why we the privilege to consider only the prime numbers below the sqrt of the given number
Hope this helps
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