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How Many Factors?

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

Factor Trees Factor Pairs Level 1 Level 2 Level 3 Level 4 Menu Help More...
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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 6 have?

Correct Wrong

List all of those factors in order:

Correct Wrong

How many factors does 8 have?

Correct Wrong

List all of those factors in order:

Correct Wrong

How many factors does 9 have?

Correct Wrong

List all of those factors in order:

Correct Wrong

How many factors does 11 have?

Correct Wrong

List all of those factors in order:

Correct Wrong

How many factors does 12 have?

Correct Wrong

List all of those factors in order:

Correct Wrong

How many factors does 16 have?

Correct Wrong

List all of those factors in order:

Correct Wrong

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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.

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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.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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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


Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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