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

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

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

There is no pattern for finding all of the prime numbers the exist, back mathematicians have discovered prime numbers with nearly eight million digits. This is among the remaining large math mysteries the end there for mathematicians.

Composite numbers have an ext than two factors yet not an infinite number of factors. All even numbers (except the number two) room composite, since they have the right to all be separated by two.

Zero is neither prime no one composite. Since any type of number times zero equals zero, there are an infinite variety of factors for a product that zero. A composite number must have actually a finite number of factors.

One is also neither prime nor composite. The only method to get a product that one is by multiply 1 x 1. Yet duplicate components are only counted once, so one only has one factor. (A prime number has exactly two factors, so one can not be prime.)

A common test question would have actually you determine which number native a list is element (or composite or neither).

Try this one:


Which of the complying with is a element number?


Reveal Answer

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

Cool Rules

Divisibility rules space tools to help you do less division. The divisibility rule can help you identify if a number is element or composite as well as aid you rest composite numbers right into their element factors, the subject we will certainly cover next.

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

Divisibility Rules

Which the the following numbers is not divisible by 3?


Reveal Answer

The exactly answer is A. The fast way to execute this trouble is to use the divisibility rule; add the number of each number looking for the one the is not a multiple of three. The slow way would be to perform each division problem—even on a calculator, this an approach will take it longer!

Prime Factorization: T’s and also Tree

This is one more topic you could not have actually thought about since middle school. The fundamental Theorem that Arithmetic says that every composite number can be damaged down right into a unique product of prime numbers.

Prime factorization is the procedure that find the prime-number assets of a given composite number. Element factorization is beneficial in its very own right, but 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. For example, 12 is 2 x 2 x 3 or 22 x 3. (Prime factorizations are often represented v exponents.)

If girlfriend can’t find the element factorization mentally, try either a Factor-T or a element Tree.


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

Step 1: determine a prime number that divides into your given number. Create that number in the left column.

Step 2: create the quotient of her number divided by the prime number in the ideal hand column.

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

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