Any number greater than one that can only be divided by itself and one is a prime number. Composite numbers have more than two divisors. Zero and one are neither prime nor composite. Following the Fundamental Theorem of Arithmetic, all integers greater than one are either prime numbers or a product of prime numbers. Learn the indicators of composite numbers to help you identify prime and composite numbers easily.

Memorize the prime numbers between two and 20. Continue to add numbers to your list until you have memorized the 25 prime numbers between two and 100. Make a chart of the 168 prime numbers between two and 1,000 to facilitate remembering the additional prime numbers.

Screen any number for signs that you have a composite number. A number ending in an even number, a five or a zero must be a composite number. An even number greater than two will divide evenly by two. Numbers ending with a five or zero divide evenly by five.

Determine whether the number is divisible by three. Any number whose digits add up to a number divisible by three is also divisible by three. With the number 213, adding the digits together gives you a sum of six, so the number is divisible by three.

Check to see if nine will evenly divide the number. Any number whose digits add up to nine or a product of nine is divisible by nine. Add all of the digits in the number 132,111 together and you get nine. With a number such as 3,564, the sum of the digits equals 18 and the sum of those digits is nine. Nine divides evenly into both 132,111 and 3,564.

Test to see if 11 will evenly divide the number. If the difference between the sum of a number’s alternating digits is divisible by 11, then the number is also divisible by 11. Using 22,649 as an example, add the alternating digits two, six and nine to get a sum of 17. Add the remaining digits, two and four for a sum of six. Subtract the two sums, 17 and six to give you a remainder of 11. You know that 22,649 is divisible by 11.

Select the closest perfect square larger than the number in question and attempt to divide the specified number evenly with all prime numbers smaller than the square root of the perfect square. If your specified number is 133, the closest perfect square larger than this number is 144 and its square root is 12. Two won’t evenly divide into 133 because it is odd. The number doesn’t end in five or zero, so you can’t divide by five. Try dividing 133 by three, seven and 11, the remaining prime numbers smaller than 12. You discover that 133 is the product of seven and 19.
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