# How Many Factors?

## Work out the number of factors a number has then write them all as a list.

##### Factor TreesFactor PairsLevel 1Level 2Level 3Level 4MenuHelpMore...

This is level 1: numbers less than 30. When you type in the list of factors separate the factors with commas. You will be awarded a trophy if you get at least 9 correct and you do this activity online.

 How many factors does 4 have? List all of those factors in order: How many factors does 7 have? List all of those factors in order: How many factors does 10 have? List all of those factors in order: How many factors does 15 have? List all of those factors in order: How many factors does 18 have? List all of those factors in order: How many factors does 20 have? List all of those factors in order:
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This is How Many Factors? level 1. You can also try:
Level 2 Level 3 Level 4

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

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## Description of Levels

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Factor Trees - This is a good place to begin finding factors.

Factor Pairs - Here are nine puzzles with clues!

Level 1 - Numbers less than 30

Level 2 - Numbers between 30 and 100

Level 3 - Numbers between 100 and 300

Level 4 - Numbers between 300 and 1000

More factor activities including lesson Starters, visual aids, investigations and self-marking exercises.

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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Example

The video above is from "Let's Do Math"

Here is a different way to calculate the number of factors a number has. It appeared in Mathematical Pie, a Mathematical Association publication.

The prime factorisation of 600 is 23 x 52 x 3. We can make all the factors of 600 by choosing from four possibilities for the 2 (to include it 0, 1, 2 or 3 times); three possibilities for the 5 (to include it 0, I or 2 times) and two possibilities for the 3 (to include it or not).

Altogether 4 x 3 x 2 = 24 possibilities (if we don't choose any of the three this will give the factor l). So 600 has 24 factors.

When you know the number of factors of a number it is also helpful to know that the factors come in pairs. For example the factors of 96, shown in their pairs, are:

1 x 96
2 x 48
3 x 32
4 x 24
6 x 16
8 x 12

Square numbers have an odd number of factors. One factor, the square root, is multiplied by itself to give the number. For example the factors of 36 are:

1 x 36
2 x 18
3 x 12
4 x 9
62

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