ISEE Upper Level Math : How to find out if a number is prime
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Example Questions
Example Question #1 : How To Find Out If A Number Is Prime
Add all of the prime numbers between 50 and 70.
The prime numbers between 50 and 70 are 53, 59, 61, and 67. Their sum is
Example Question #2 : How To Find Out If A Number Is Prime
Add all of the prime numbers between 20 and 40.
The prime numbers between 20 and 40 are 23, 29, 31, and 37.
Their sum is 
Example Question #3 : How To Find Out If A Number Is Prime
Which of these numbers is prime?
A prime number has exactly two factors, 1 and itself. We can eliminate four choices by finding other factors:
53 has only 1 and 53 as factors, so it is the only prime among the choices.
Example Question #4 : How To Find Out If A Number Is Prime
How many composite numbers are between 61 and 80 inclusive?
There are twenty integers from 61 to 80 inclusive. Counting composite numbers can be made easier by weeding out the primes - 61, 67, 71, 73, 79. Removal of these five primes leave fifteen composite numbers.
Example Question #5 : How To Find Out If A Number Is Prime
Which of the following numbers is prime?
The correct answer is 
First, find the approximate square root of the number:
We know this because:
Therefore, we only need to consider prime numbers through
Is 
We know this because:
Therefore, we need to consider the followig prime numbers:
Is 
Example Question #6 : How To Find Out If A Number Is Prime
How many composite numbers are between and
inclusive?
There are twenty integers from to
inclusive. Counting composite numbers can be made easier by weeding out the primes -
. Removal of these five primes leaves
Example Question #7 : Prime Numbers
Which of the following numbers is prime?
The correct answer to this question is 
Next, determine if the number is divisible by any prime numbers up to and including the square root. In this instance consider the numbers:
Example Question #5 : How To Find Out If A Number Is Prime
How many composite numbers are between 
There are thirty integers from 
Example Question #3 : How To Find Out If A Number Is Prime
Reduce the fraction:
First, given that 13 times 4 is 52, the numerator can be simplified by taking the square root of 4 and multiplying it by the square root of 13.
Example Question #6 : How To Find Out If A Number Is Prime
How many prime numbers are there between 1 and 20?
11
9
2
8
7
8
A prime number is one in which only itself and 1 can go into it. Therefore, 2, 3, 5, 7, 11, 13, 17, and 19 are the only prime numbers in that set.
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