A prime number is made up of only two factors: one and itself. A composite number is made up of **more than two elements**. There is no prime or composite number greater than one. Because each of these numbers has just two components, itself and 1, the prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. None of these numbers are composite.

- Which lists all the factors of a composite number?
- Is a composite number greater than 1?
- Can composite numbers have more than one prime factorization?
- Why are all even numbers composite?
- Can a composite number have five factors?
- What is the least number of factors that a number can have?
- Is 9 a composite number?
- What is a composite number for kids?

Other than one and the number itself, a composite number has more than two elements. In this case, 2 has only two factors: 1 and 2. Therefore, it is not a prime number.

We discovered the factors of a number in the previous section. There are just two elements in **prime numbers**: the number 1 and the prime number itself. Every composite number has more than two factors, and every composite number is a unique product of primes. This is known as a number's prime factorization. The number 6 has several different prime factorizations: 2 × 3 × 3, 2 × 2 × 3, 2 × 2 × 2, 3 × 3 × 7, and so on.

It is possible to give any positive integer its own special prime factorization. For example, the factorization of 60 includes **5 factors**, each of which is divisible by 2 but not by 3: 2, 2, 2, 2, 2, 3, 5, 10, 15, 30. However, these are not the only possibilities. Any positive integer can have **an arbitrary prime factorization**. That is why there are many different ways to write the same number.

In mathematics, especially algebra, it is common to specify an expression using parenthesized sets of factors, called a factoring scheme. For example, the fact that 6 divides into 2 × 3 × 3 implies that there must be some other number r such that 0 < r ≤ 3 and r divides into 6. Thus, r = 2 is a valid solution. This means that there are actually two different factorizations for 6: 2 × 3 × 3 and 2 × 2 × 2.

A prime number is a whole number with just two factors: itself and one. A composite number includes components other than one and itself. Neither 0 nor 1 are prime or composite numbers. Because all even numbers are divisible by two, every even number bigger than two is a composite number.

When a number contains only two components, one and itself, it is said to be prime. When a number includes more than two elements, it is referred to as a composite... Definitions

factors of 2: | 1 x 2 | 2 is prime |
---|---|---|

factors of 5: | 1 x 5 | 5 is prime |

factors of 6: | 1 x 6, 2 x 3 | 6 is composite |

factors of 7: | 1 x 7 | 7 is prime |

factors of 8: | 1 x 8, 2 x 4 | 8 is composite |

So, no, the smallest number of variables that a number may have is one, not two. And, sure, calculating the components can tell you if a number is prime, composite, or equal to 1. Because 0*k = 0 for **any k**, it is termed a composite number with an unlimited number of components.

A prime number is an integer, or whole number, that has only two factors, 1 and itself. Put another way, a prime number can be divided evenly only by 1 and by itself. Prime numbers also must be greater than 1. For example, 3 is a prime number because 3 cannot be divided evenly by **any number** except for 1 and 3.

This is not the case (i.e., which has factors other than 1 and itself). The first several composite numbers (often abbreviated as "composites") are 4, 6, 8, 9, 10, 12, 14, 15, 16. After this point, only prime numbers continue to be composites.

All positive integers except one are composite: if n is positive then it can be written as a product of primes, and no number other than 1 can be written as a product of primes. Therefore, all positive integers except 1 are composites.

Even though 9 is not a prime number, it can be written as a product of **two primes**: 3 and 3. Thus, every integer divisible by 9 is composed.

Whole numbers that can be split by numbers other than themselves and one are known as composite numbers. They've got "factors." The numbers that divide it are known as factors. Every whole number greater than one is classified as either a composite number or a prime number. Composite numbers can be expressed as a product of two smaller numbers, while primes are only divisible by 1 and themselves.

Composite numbers include numbers that you might expect: 2, 3, 4, 5, 6, 7, 8, 9, 10. However, there are also some very large composite numbers, such as the number given above - which is equal to 1 million million (or 1 trillion) - that have many factors larger than themselves. These large numbers are called composite numbers because they are made up of **multiple smaller numbers** that when multiplied together give the original number.

Prime numbers are numbers that have only 1 and themselves as factors. Because there are more prime numbers than composite numbers, most integers are composites. The only exception is when an integer is factored into **a single factor** which is then necessarily itself equal to 1. In **this case**, the number is said to be prime.

Factoring is the process of dividing integers into **their prime factors**.