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:ģ = (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. If you are curious about what prime and composite numbers are, get ready… We are set to learn great things about these infinitely amazing numbers! Prime and composite numbersĪ factor of a natural number is a positive divisor of it. That a number can be written in a unique way using primes, is one of the most important properties of primes numbers, because they basically give an ID to each integer greater than 1. For example, 54 = 6 × 9 and 54 = 2 × 3 × 9 are different ways of writing 54 as a product of factors but, 54 = 2× 3 × 3 × 3 is a unique way using prime numbers!
Prime or Composite Game (Alternate Version).Determine whether a given whole number in the range 1 to 100 is prime or composite. Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. Recognize that a whole number is a multiple of each of its factors. The resources below are similarly aligned.įind all factor pairs for a whole number in the range 1 to 100. The Factors and multiples Chart above is aligned, either partially or wholly, with the standard 4OA04 from the Common Core Standards For Mathematics (see the shortened extract below).