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Number seven is a very interesting number that appears in many places! There are 7 days in a week, 7 wonders of the world, 7 continents, and 7 colors in the rainbow, just to mention some.
In mathematics, 7 is also a very special number that has amazing particular properties. One of them is that 7 is a prime number, as we will verify next.
We will start recalling some definitions that we have widely discussed in our Prime Numbers article. If you still feel unfamiliar with these notions, we invite you to first read that article and come back here later.
A factor of a natural number is a positive divisor of the number. A proper factor of a natural number is a factor that is different from 1 and from the number itself. For example, 14 = 2 × 7 = 1 × 14; thus, 1, 2, 7 and 14 are all factors of 14, but only 2 and 7 are proper factors of 14.
A natural number is called prime number if it is greater than 1, and it doesn’t have proper factors. For example, the prime numbers less than 7 are 2, 3, and 5.
Seven is a prime number because it doesn’t have proper factors. In other words, the only factors of 7 are 1 and itself. To be sure of this, let’s verify that none of the numbers greater than 1 and less than 7 divides 7.
The numbers greater than 1 and less than 7 are 2, 3, 4, 5, and 6.
Therefore, 7 can only be written as the product 1 × 7 = 7. Meaning that its only factors are 1 and itself. Thus, 7 is a prime number.
On the other hand, prime numbers cannot be split into equal parts, each having more than one element. This is another way of verifying that 7 is a prime number:
Example: Is 27 a prime number?
To answer this question, we should verify if 27 has proper factors. We know that 27 = 3 × 9. Thus, 27 has two proper factors: 3 and 9. This means that 27 is not a prime number!
Also, notice that 27 can be split into three equal parts, each having more than one element. This can only be done because 27 is not a prime number.
There are many different classes of prime numbers. We will name three of them here, and then we will see to which of these classes number 7 belongs.
The amazing 7 is the only prime number belonging to the three of these classes. Let’s find out why:
We invite you to read other articles on prime numbers, on our blog, to find out which other prime numbers belong to these classes.
How do you think 2 is a composite number?
Yes, because its only factors are 1 and itself.
No, because it doesn’t have proper factors.
Yes, because it is of the form 7=(2×3)+1, where 2 and 3 are the first two prime numbers.
Yes, because it is of the form $$7\;=\;2^3\;–\;1.$$
Yes, because it is of the form 7=2(3)+1, where 3 is prime.
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