How to determine whether a number is a prime or composite number
What is the difference between a prime and composite number?
You’ve already learned several ways to classify a whole number: as positive, negative, or ???0???; as the opposite of a number, in terms of the whole numbers by which it’s divisible, and in terms of its multiples.
Another way to classify a whole number greater than ???1??? is as either a “prime” number or a “composite” number. A whole number will either be a prime number or a composite number, but it can’t be both.
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A prime number is a whole number greater than ???1??? that’s divisible by only ???1??? and itself. We already know that every whole number is divisible by ???1???, because if you divide any whole number by ???1???, you’ll get the original number as the result. Here are some examples:
???10\div1=10???
???7\div1=7???
???316\div1=316???
And every whole number other than ???0??? is divisible by itself, because if you divide any whole number other than ???0??? by itself, you’ll get ???1??? (a whole number) as the result. Here are some examples:
???10\div10=1???
???7\div7=1???
???316\div316=1???
Prime numbers are special because they are divisible by only ???1??? and themselves. As an example, ???7??? is a prime number because it’s divisible by ???1??? (???7\div1=7???) and by itself (???7\div7=1???), but not by anything else. It’s not divisible by ???2???, ???3???, ???4???, ???5???, or ???6???, because none of these numbers divides evenly into ???7???.
The number ???11??? is also a prime number, because the only numbers that divide evenly into ???11??? are ???1??? and ???11???.
Because ???7??? and ???11??? are divisible only by ???1??? and themselves, we call them “prime” numbers.
Contrast this with composite numbers, which by definition are numbers greater than ???1??? that are divisible by something other than just ???1??? and themselves. For example, ???6??? is a composite number; it’s divisible by ???1??? (???6\div1=6???) and by itself (???6\div6=1???), but it’s also divisible by ???2??? (???6\div2=3???) and by ???3??? (???6\div3=2???). Because ???6??? is divisible by more than just ???1??? and itself, we call it a “composite” number.
How to determine whether a number is a prime number or a composite number
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Say whether the number is a prime number or composite number
Example
Say whether ???21??? is prime or composite.
The number ???21??? is divisible by ???1??? (???21\div1=21???) and by itself (???21\div21=1???), but it’s also divisible by ???3??? (???21\div3=7???) and by ???7??? (???21\div7=3???). Because ???21??? is divisible by more than just ???1??? and itself, it’s a composite number, not a prime number.
