A prime number is divisible by exactly two positive whole numbers: 1 and the number itself. A composite number is divisible by at least three numbers.
For example, 2 is a prime number because when you divide it by any number but 1 and 2, you get a remainder. So there’s only one way to multiply two counting numbers and get 2 as a product:Similarly, 3 is prime because when you divide by any number but 1 or 3, you get a remainder. So the only way to multiply two numbers together and get 3 as a product is the following:
On the other hand, 4 is a composite number because it’s divisible by three numbers: 1, 2, and 4. In this case, you have two ways to multiply two counting numbers and get a product of 4:
But 5 is a prime number because it’s divisible only by 1 and 5. Here’s the only way to multiply two counting numbers and get 5 as a product:
And 6 is a composite number because it’s divisible by 1, 2, 3, and 6. Here are two ways to multiply two counting numbers and get a product of 6:
Every counting number except 1 is either prime or composite. The reason 1 is neither is that it's divisible by only one number, which is 1.
Here's a list of the prime numbers that are less than 30:2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Remember the first four prime numbers: 2, 3, 5, and 7. Every composite number less than 100 is divisible by at least one of these numbers. This fact makes it easy to test whether a number under 100 is prime: Simply test it for divisibility by 2, 3, 5, and 7. If it's divisible by any of these numbers, it's composite — if not, it's prime.
For example, suppose you want to find out whether the number 79 is prime or composite without actually doing the division. Here's how you think it out:-
79 is an odd number, so it isn't divisible by 2.
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79 has a digital root of 7 (because 7 + 9 = 16; 1 + 6 = 7), so it isn't divisible by 3.
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79 doesn't end in 5 or 0, so it isn't divisible by 5.
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Even though there's no trick for divisibility by 7, you know that 77 is divisible by 7. So, 79 ÷ 7 leaves a remainder of 2, which tells you that 79 isn't divisible by 7.
Now test whether 93 is prime or composite:
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93 is an odd number, so it isn't divisible by 2.
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93 has a digital root of 3 (because 9 + 3 = 12 and 1 + 2 = 3), so 93 is divisible by 3.