Basic number theory

Get a strong understanding of the very basic of number theory. Life is full of patterns, but often times, we do not realize as much as we should that mathematics too is full of patterns.


If I show you the following list: 2, 4, 6, 8, 10,...

You may immediately conclude that the next number after 10 is 12.

If I show you also the following list:

2 × 1, 2 × 2, 2 × 3, 2 × 4,...

What comes next?

Of course it is 2 × 5

Exploring number patterns can really help you develop a strong understanding of mathematics concepts. It is my desire that you develop a love for this topic and others to come.

In this unit, you will explore some other interesting patterns while I teach the following topics:

Identify prime and composite numbers.

Find least common multiple

find greatest common factor.

Find multiples for a given number

Divisibility tests

To use sets of numbers to find and describe number patterns

Problems that can be solved with number theory:

Example #1:

What is the least number of marbles that can satisfy the following situation:

Put the marbles in 2 piles with no leftovers

Put the marbles in 5 piles with no leftovers

Put the marbles in 7 piles with no leftovers

To solve this problem, you can play around with the marbles until you find the correct combination


However, you could get the least common multiple of 2, 5, and 7.

LCM (2,5,7) = 70

You need 70 marbles

Example #2:

Your father wants to give you some money if the following condition is met

You can share the money with either 2, 3, or 6 people

The money is less than 100 dollars

You need divisibility rules to solve this problem. There may be more than one solution

All you have to do is to make sure that the number is divisible by 2, 3, and 6 at the same time

Possible solutions: 42, 12, and 84

Example #3:

A clown waves at people every 3 minutes
A second clown waves every 4 minutes
A third clown waves every 5 minutes
When will all 3 clowns wave at the same time?

Just get the least common multiple of 3, 4, and 5

LCM(3,4,5) = 60

All clowns will wave at the same time in 60 minutes

Now test yourself to see if you understood the lesson on this page with the quiz below.









Now dig deeper with the following number theory lessons

 Homepage                            

 Number theory 

 Greatest common factor

 Learn to get the greatest common factor of two numbers

 Counting factors

 How many factors can a number have?

 Least common multiple

 Learn how we found the least common multiple for example #3 and  others.

 Prime number

 What is a prime number?

 Prime numbers chart

 Divisibility rules

 How to quickly tell if a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, and 10

 Amicable numbers

 Perfect numbers


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