Math Basics: Prime Numbers

When you think of prime numbers, it takes you back to younger school days, doesn’t it! However, it is surprising that many test takers are still not very familiar with the concept of prime numbers. So, before you go on to the more advanced stuff in math, read this post to brush up on your basics.

A prime number is a number which has just two factors: itself and 1. Or in other words it can be divided evenly only by itself and 1. For instance, 3 is a prime number because it can be divided evenly only by itself and one. On the other hand, 6 can be divided evenly by 1, 2, 3 and 6. Hence, the number 6 is not a prime number.

The number 1 is not a prime number and is pretty unique in that sense. This can be easily explained with the first definition. The number one is not prime because it has only one factor: itself. A prime number typically is always a whole number greater than 1 (There are Gaussian primes as well which deal with integers).

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For exam purposes, it is a good idea to memorize the first few prime numbers. They are 2, 3, 5, 7, 11, 13, 17, 19 and so on. The number 2 is the only even prime number.

Sometimes in an exam-scenario, you would be faced with a situation to determine whether a number is prime or composite. While it is relatively simple to do this for small numbers, it is not so easy for 3-digit and larger numbers. In order to solve this quickly, there are some simple divisibility rules to determine whether the numbers are prime or composite.

Here are some divisibility rules for prime numbers:

  • If the number is even, it will always be divisible by 2
  • If the sum of the digits is divisible by 3, the number will be divisible by 3
  • If the number ends with 5 or 0, it will be divisible by 5
  • Double the last digit and subtract it from the rest of the number. If the answer is divisible by 7, the original number will be divisible by 7
  • Add alternate digits and subtract it from the difference of the next sum of alternate digits, For instance, if the number is 574652, add 5+4+5=14 and 7+6+2=15. If the difference i.e. 1 is divisible by 11, then the number will be divisible by 11. In this case, clearly the number is not divisible by 11.

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