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Arithmetic: Primes and Divisibility |
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A prime number is a number that can be divided evenly by only itself and 1. For example, 3 is a prime number because it can only be divided by 3 and 1 without a remainder, but 6 is not a prime number, because 6 can be divided by 1, 2, 3, and 6. The numbers 0 and 1 are NOT prime numbers, by definition. The number 2 is special because it is the only even number that is a prime number. GRE questions will often ask you to count the number of 'primes' in a range of numbers.
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For example, the first 15 positive prime numbers, starting with 2, are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. Should you memorize these? NO! But you should be able to look at a number and determine if it is not a prime number. If the number can be divided by 2, 3, 4, 5, ..., etc, or by any number other than itself and 1, then it is NOT prime. |
If there are two numbers and the first number can be divided evenly by the second number, then the first number is divisible by the second number. For example, 25 is divisible by 5, because you can divide 25 by 5 with no remainder. In this example, 5 is also called a 'factor' of 25, because it can divide into 25 evenly. As another example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.
In addition, prime factors are numbers which are both factors of a number and which are prime. Of 36, 2 and 3 are the only prime factors; 4, 6, 9, 12 and 18 are not prime factors of 36, because these are not prime numbers.
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