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

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Previously CoveredSo far, we’ve spanned the various varieties of number (real numbers, rational numbers, irrational numbers, whole numbers, and integers), as well as how they relate to each other using the common an equipment of a number line.We’ve also discussed the various properties of enhancement and multiplication.All totality numbers room categorized together either element or composite, v the exceptions of zero and also one, which are special cases. Let’s take it a look at the difference between prime and composite numbers. Element numbers have specifically two factors, one and the number itself. If you understand your divisibility rule (covered in the next section), climate determining the element numbers indigenous 1–100 is a fairly easy task. Below are the element numbers approximately 25:

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

There is no pattern for finding all of the element numbers the exist, although mathematicians have uncovered prime numbers with virtually eight million digits. This is one of the remaining big math mysteries the end there because that mathematicians.

Composite numbers have more than 2 factors but not an infinite variety of factors. All also numbers (except the number two) are composite, since they deserve to all be separated by two.

Zero is no prime no one composite. Since any type of number times zero equals zero, there room an infinite number of factors for a product the zero. A composite number must have actually a finite variety of factors.

One is likewise neither prime no one composite. The only means to gain a product that one is by multiplying 1 x 1. But duplicate components are just counted once, for this reason one only has actually one factor. (A prime number has exactly two factors, so one can not be prime.)

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

Try this one:


Which of the adhering to is a prime number?


Reveal Answer

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

Cool Rules

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

Divisibility rules space shortcuts to tell friend if one number is divisible by one more number. The rule cover department by numbers 2–10 and allow you to examine numbers up through 100. Click the number in the chart.

Divisibility Rules

Which of the adhering to numbers is not divisible by 3?


Reveal Answer

The exactly answer is A. The fast way to perform this problem is to usage the divisibility rule; add the digits of every number looking for the one the is not a multiple of three. The slow means would it is in to do each division problem—even top top a calculator, this technique will take it longer!

Prime Factorization: T’s and also Tree

This is an additional topic you might not have thought around since center school. The basic Theorem of Arithmetic says that every composite number can be damaged down into a distinct product of prime numbers.

Prime factorization is the process that find the prime-number products of a provided composite number. Prime factorization is helpful in its own right, but many of the applications because that it show off fractions, which fine cover down the road.

You may have the ability to find a number’s element factorization in your head. Because that example, 12 is 2 x 2 x 3 or 22 x 3. (Prime factorizations are often represented v exponents.)

If friend can’t uncover the prime factorization mentally, try either a Factor-T or a element Tree.


In a Factor-T, friend will have actually two columns: the left obelisk with the element numbers and the right shaft with significantly smaller quotients native division.

Step 1: identify a element number that divides into your given number. Write that number in the left column.

Step 2: create the quotient of your number divided by the prime number in the best hand column.

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Step 3: now look because that a prime number that divides right into the quotient, 39 in this case. Continue steps 1 and also 2 till you have a one in the right-hand column. The number on the left are your prime factorization!

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