In this lesson we will review prime and composite numbers. We’ll also review some handy rules the make division faster and also easier.

You are watching: Which number is neither prime nor composite

Previously CoveredSo far, we’ve spanned the various species of numbers (real numbers, reasonable numbers, irrational numbers, whole numbers, and also integers), as well as how they relate to each other using the common device of a number line.We’ve additionally discussed the assorted properties of addition and multiplication.All whole numbers are categorized as either element or composite, with the exception of zero and also one, which space special cases. Let’s take a look in ~ the difference in between prime and composite numbers. Element numbers have exactly two factors, one and also the number itself. If you understand your divisibility rules (covered in the next section), climate determining the prime numbers native 1–100 is a relatively easy task. Below are the element numbers approximately 25:

2, 3, 5, 7, 11, 13, 17, 19, 23

There is no pattern because that finding every one of the element numbers that exist, although mathematicians have found prime number with virtually eight million digits. This is among the remaining large math mysteries the end there because that mathematicians.

Composite numbers have much more than two factors however not one infinite number of factors. All even numbers (except the number two) space composite, since they can all be separated by two.

Zero is no prime nor composite. Since any kind of number time zero amounts to zero, there room an infinite variety of factors because that a product that zero. A composite number must have a finite variety of factors.

One is likewise neither prime no one composite. The only way to obtain a product that one is by multiply 1 x 1. Yet duplicate components are just counted once, for this reason one only has one factor. (A element number has specifically two factors, for this reason one can’t be prime.)

A typical test inquiry would have you identify which number indigenous a perform is element (or composite or neither).

Try this one:


Which of the following is a prime number?


Reveal Answer

The exactly answer is C. Forty-one is a prime number; the other numbers room composite. Be mindful with 51—it comes from 3 x 17.

Cool Rules

Divisibility rules space tools to aid you do much less division. The divisibility rule can help you determine if a number is element or composite too as help you rest composite numbers into their element factors, the topic we will cover next.

Divisibility rules room shortcuts come tell friend if one number is divisible by an additional number. The rules cover division by number 2–10 and permit you to examine numbers up through 100. Click the number in the chart.

Divisibility Rules

Which the the complying with numbers is not divisible through 3?


Reveal Answer

The exactly answer is A. The fast method to perform this trouble is to use the divisibility rule; include the number of each number searching for the one the is not a multiple of three. The slow method would it is in to carry out each division problem—even on a calculator, this technique will take longer!

Prime Factorization: T’s and Tree

This is another topic you could not have actually thought around since middle school. The basic Theorem the Arithmetic claims that every composite number deserve to be broken down right into a unique product of prime numbers.

Prime factorization is the process that find the prime-number assets of a provided composite number. Prime factorization is useful in its very own right, however many of the applications for it involve fractions, which fine cover down the road.

You may be able to find a number’s prime factorization in her head. Because that example, 12 is 2 x 2 x 3 or 22 x 3. (Prime factorizations are often represented through exponents.)

If you can’t discover the prime factorization mentally, try either a Factor-T or a aspect Tree.


In a Factor-T, friend will have actually two columns: the left obelisk with the prime numbers and also the right column with increasingly smaller quotients native division.

Step 1: recognize a prime number the divides right into your offered number. Write that number in the left column.

Step 2: create the quotient of her number split by the prime number in the best hand column.

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Step 3: currently look for a element number the divides into the quotient, 39 in this case. Proceed steps 1 and 2 till you have actually a one in the right-hand column. The number on the left room your prime factorization!

The prime factorization of 78 is 2 x 3 x 13. No various other number has this prime factorization.