In other words, 21 is not a prime number.Īs we see, the concept of “prime number” is linked to that of “composite number” because any natural number greater than 1 is either prime or composite. Meaning that both 3 and 7 are proper factors of 21, thus 21 is a composite number. We continue with 3, and we notice that 21 = 3 × 7. Since 21 is not even, 2 doesn’t divide 21. But, where do we look for proper factors? In the list: 2, 3, 4, 5, 6, 7, 8, …, 19, 20, of all natural numbers greater than 1, and less than 21. To answer this question, we should verify if 21 has proper factors.
For example, 9 is an odd number, but it can be split into three equal parts of more than one element. We are not claiming that every odd number is a prime number. Contrarily, the prime number 3 can only be split into equal parts, if each part has one element. Number 6 is composed of numbers different from itself, but 3 is not.Īnother way of differentiating a composite number from a prime number is noticing that a composite number can be split into equal parts having more than one element, but a prime number cannot.įor example, 6 can be split into 2 parts with 3 elements each or into 3 parts with 2 elements each, as shown below. The difference between 3 and 6 is like in the image: 3 comes alone to the party, and 6 comes with two of its friends: the proper factors 2 and 3. Number 6, instead, has two proper factors: 2 and 3, because 6 = 2 × 3. Let’s explore more differences between prime and composite numbers.įor example, 3 = 1 × 3 doesn’t have proper factors, because 2 doesn’t divide it: 3 = (2×1) + 1. Thus, 2 doesn’t have proper factors, and it is, therefore, a prime number.Ī composite number is a natural number that has proper factors. For example, the only factors of 2 are 1 and 2. Thus, the proper factors of 8 are 2 and 4.Ī natural number is called a prime number if it is greater than 1, and it doesn’t have proper factors. Moreover, a proper factor of a natural number is a factor that is different from 1 and from the number itself. For example, the factors of 8 are 1, 2, 4, and 8, because 8 = 8 × 1 = 2 × 4. A factor of a natural number is a positive divisor of it.
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