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Listing Factors

Introduction

Terms

Factor - A number that evenly divides into another without leaving a remainder.

Lesson

When we are asked to list all the factors of a number, we are being asked to simply list all the numbers that can evenly divide (i.e. leave no remainder) into the given number. So if we are given 25, we first determine all the factors of 25:

125=251 * 25 = 25

55=255 * 5 = 25

251=2525 * 1 = 25

And then we just list them as the answer: 1, 5, 25.

Note that the 5 only gets listed once!

Similarly, when asked to list the factors for 44, we get:

144=441*44=44

222=442*22=44

411=444*11=44

114=4411*4=44

222=4422*2=44

441=4444*1=44

So the factors of 44 are 1,2,4,11,22,441, 2, 4, 11, 22, 44

Examples

Listing Factors (Example #1)

2424
We need to find all whole number pairs whose product is 24
124=241 * 24 = 24
212=242 * 12 = 24
38=243 * 8 = 24
46=244 * 6 = 24
The factors of 2424 are 1,2,3,4,6,8,12 and 241, 2, 3, 4, 6, 8, 12\text{ and }24

Listing Factors (Example #2)

2929
We need to find all whole number pairs whose product is 29
129=291 * 29 = 29
The factors of 2929 are 1 and 291\text{ and }29

Listing Factors (Example #3)

3232
We need to find all whole number pairs whose product is 32
132=321 * 32 = 32
216=322 * 16 = 32
48=324 * 8 = 32
The factors of 3232 are 1,2,4,8,16 and 321, 2, 4, 8, 16\text{ and }32

Listing Factors (Example #4)

6464
We need to find all whole number pairs whose product is 64
164=641 * 64 = 64
232=642 * 32 = 64
416=644 * 16 = 64
The factors of 6464 are 1,2,4,8,16,32 and 641, 2, 4, 8, 16, 32\text{ and }64

Listing Factors Worksheets (PDF)

Listing Factors Worksheet 1

Listing Factors Worksheet 2

Listing Factors Worksheet 3

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