*This Math quiz is called 'Factors and Common Factors' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

* It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us*

A factor is a number that can be evenly divided into other whole number without having a remainder left over. For example, 5 is a common factor of 5, 10, 15, 20, 25, etc. Whole numbers begin at “0” and continue through infinity. Fractions and decimals are not found in common factors making finding common factors rather easy.

A common factor is a number that can be evenly divided into a collection or series of whole numbers. For example, the number 1 is a common number that can be evenly divided into any series of whole numbers.

Finding the factors of a whole number begins with starting with the number “1” and then dividing it with the given number. For example, let’s say that our given whole number is “6”.

6 ÷ 1 = 6

We see that when we divide “6” by “1” we get a whole number, i.e., “6”. We then continue to divide the number “6” with each ascending number as follows:

6 ÷ 2 = 3

6 ÷ 3 = 2

6 ÷ 4 = 1.5

6 ÷ 5 = 1.2

6 ÷ 6 = 1

Once you divide the whole number into itself, this will give you **the last factor**. The last factor of 6 is “6”.

The factors of 6 are then, **1, 2, 3 and 6** because the answer derived is a whole number. 4 and 5 are not factors because they did not divide evenly and the answer included either a fraction or decimal.

1.

For the whole number given below, find the right answer that lists all of the number’s factors.

21

21

1, 7, 21

1, 3, 7, 21

1, 3, 7, 9, 21

1, 3, 9, 21

2.

For the whole number given below, find the right answer that lists all of the number’s factors.

24

24

1, 2, 3, 4, 6, 8, 12, 24

1, 2, 3, 4, 6, 12, 24

1, 2, 4, 6, 8, 12, 24

1, 2, 3, 4, 8, 12, 24

24 ÷ 1 = 24; 24 ÷ 2 = 12; 24 ÷ 3 = 8; 24 ÷ 4 = 6; 24 ÷ 5 = 4.8; 24 ÷ 6 = 4; 24 ÷ 7 = 3.42; 24 ÷ 8 = 3; 24 ÷ 9 = 2.66; 24 ÷ 10 = 2.4; 24 ÷ 11 = 2.18; 24 ÷ 12 = 2; 24 ÷ 13 = 1.84; 24 ÷ 14 = 1.71; 24 ÷ 15 = 1.6; 24 ÷ 16 = 1.5; 24 ÷ 17 = 1.41; 24 ÷ 18 = 1.33; 24 ÷ 19 = 1.26; 24 ÷ 20 = 1.2; 24 ÷ 21 = 1.14; 24 ÷ 22 = 1.09; 24 ÷ 23 = 1.04; 24 ÷ 24 = 1

The factors of 24 are**1, 2, 3, 4, 6, 8, 12** and **24**

The factors of 24 are

3.

For the whole number given below, find the right answer that lists all of the number’s factors.

36

36

1, 2, 3, 6, 9, 12, 36

1, 2, 3, 4, 6, 12, 36

1, 2, 3, 4, 5, 9, 18, 36

1, 2, 3, 4, 6, 9, 12, 18, 36

36 ÷ 1 = 36; 36 ÷ 2 = 18; 36 ÷ 3 = 12; 36 ÷ 4 = 9; 36 ÷ 5 = 7.2; 36 ÷ 6 = 6; 36 ÷ 7 = 5.14; 36 ÷ 8 = 4.5; 36 ÷ 9 = 4; 36 ÷ 10 = 3.6; 36 ÷ 11 = 3.27; 36 ÷ 12 = 3; 36 ÷ 13 = 2.76; 36 ÷ 14 = 2.57; 36 ÷ 15 = 2.4; 36 ÷ 16 = 2.25; 36 ÷ 17 = 2.11; 36 ÷ 18 = 2; 36 ÷ 19 = 1.89; 36 ÷ 20 = 1.8; 36 ÷ 21 = 1.71; 36 ÷ 22 = 1.63; 36 ÷ 23 = 1.56; 36 ÷ 24 = 1.5; 36 ÷ 25 = 1.44; 36 ÷ 26 = 1.38; 36 ÷ 27 = 1.33; 36 ÷ 28 = 1.28; 36 ÷ 29 = 1.24; 36 ÷ 30 = 1.2; 36 ÷ 31 = 1.16; 36 ÷ 32 = 1.12; 36 ÷ 33 = 1.09; 36 ÷ 34 = 1.05; 36 ÷ 35 = 1.02; 36 ÷ 36 = 1

The factors of 36 are**1, 2, 3, 4, 6, 9, 12, 18** and **36**

The factors of 36 are

4.

For the whole number given below, find the right answer that lists all of the number’s factors.

18

18

1, 2, 3, 9, 18

1, 2, 3, 6, 10, 18

1, 2, 6, 9, 10, 18

1, 2, 3, 6, 9, 18

18 ÷ 1 = 18; 18 ÷ 2 = 9; 18 ÷ 3 = 6; 18 ÷ 4 = 4.5; 18 ÷ 5 = 3.6; 18 ÷ 6 = 3; 18 ÷ 7 = 2.57; 18 ÷ 8 = 2.25; 18 ÷ 9 = 2; 18 ÷ 10 = 1.8; 18 ÷ 11 = 1.63; 18 ÷ 12 = 1.5; 18 ÷ 13 = 1.38; 18 ÷ 14 = 1.28; 18 ÷ 15 = 1.2; 18 ÷ 16 = 1.12; 18 ÷ 17 = 1.05; 18 ÷ 18 = 1

The factors of 18 are**1, 2, 3, 6, 9** and **18**

The factors of 18 are

5.

For the whole number given below, find the right answer that lists all of the number’s factors.

27

27

1, 2, 3, 9, 27

1, 3, 9, 27

1, 3, 6, 9, 27

1, 3, 9, 12, 27

27 ÷ 1 = 27; 27 ÷ 2 = 13.5; 27 ÷ 3 = 9; 27 ÷ 4 = 6.75; 27 ÷ 5 = 5.4; 27 ÷ 6 = 4.5; 27 ÷ 7 = 3.85; 27 ÷ 8 = 3.37; 27 ÷ 9 = 3; 27 ÷ 10 = 2.7; 27 ÷ 11 = 2.45; 27 ÷ 12 = 2.25; 27 ÷ 13 = 2.07; 27 ÷ 14 = 1.92; 27 ÷ 15 = 1.8; 27 ÷ 16 = 1.68; 27 ÷ 17 = 1.58; 27 ÷ 18 = 1.5; 27 ÷ 19 = 1.42; 27 ÷ 20 = 1.35; 27 ÷ 21 = 1.28; 27 ÷ 22 = 1.22; 27 ÷ 23 = 1.17; 27 ÷ 24 = 1.12; 27 ÷ 25 = 1.08; 27 ÷ 26 = 1.03; 27 ÷ 27 = 1

The factors of 27 are**1, 3, 9** and **27**

The factors of 27 are

6.

For the whole number given below, find the right answer that lists all of the number’s factors.

19

19

1, 3, 19

1, 3, 4, 19

1, 7, 19

1, 19

19 ÷ 1 = 19; 19 ÷ 2 = 9.5; 19 ÷ 3 = 6.33; 19 ÷ 4 = 4.75; 19 ÷ 5 = 3.8; 19 ÷ 6 = 3.16; 19 ÷ 7 = 2.71; 19 ÷ 8 = 2.37; 19 ÷ 9 = 2.11; 19 ÷ 10 = 1.9; 19 ÷ 11 = 1.72; 19 ÷ 12 = 1.58; 19 ÷ 13 = 1.46; 19 ÷ 14 = 1.35; 19 ÷ 15 = 1.26; 19 ÷ 16 = 1.18; 19 ÷ 17 = 1.11; 19 ÷ 18 = 1.05; 19 ÷ 19 = 1

The factors of 19 are**1** and **19**

The factors of 19 are

7.

For the whole number given below, find the right answer that lists all of the number’s factors.

9

9

3, 9

1, 9

1, 3, 9

1, 3, 6, 9

9 ÷ 1 = 9; 9 ÷ 2 = 4.5; 9 ÷ 3 = 3; 9 ÷ 4 = 2.25; 9 ÷ 5 = 1.8; 9 ÷ 6 = 1.5; 9 ÷ 7 = 1.28; 9 ÷ 8 = 1.12; 9 ÷ 9 = 1

The factors of 9 are**1, 3** and **9**

The factors of 9 are

8.

For the whole number given below, find the right answer that lists all of the number’s factors.

12

12

1, 2, 3, 4, 6, 10, 12

1, 2, 3, 4, 6, 12

1, 2, 3, 4, 10, 12

1, 2, 4, 6, 12

12 ÷ 1 = 12; 12 ÷ 2 = 6; 12 ÷ 3 = 4; 12 ÷ 4 = 3; 12 ÷ 5 = 2.4; 12 ÷ 6 = 2; 12 ÷ 7 = 1.71; 12 ÷ 8 = 1.5; 12 ÷ 9 = 1.33; 12 ÷ 10 = 1.2; 12 ÷ 11 = 1.09; 12 ÷12 = 1

The factors of 12 are**1, 2, 3, 4, 6** and **12**

The factors of 12 are

9.

For the whole number given below, find the right answer that lists all of the number’s factors.

16

16

1, 2, 3, 4, 8, 16

1, 2, 4, 6, 8, 16

1, 2, 4, 8, 16

1, 2, 3, 6, 8, 16

16 ÷ 1 = 16; 16 ÷ 2 = 8; 16 ÷ 3 = 5.33; 16 ÷ 4 = 4; 16 ÷ 5 = 3.2; 16 ÷ 6 = 2.66; 16 ÷ 7 = 2.28; 16 ÷ 8 = 2; 16 ÷ 9 = 1.77; 16 ÷ 10 = 1.6; 16 ÷ 11 = 1.45; 16 ÷ 12 = 1.33; 16 ÷ 13 = 1.23; 16 ÷ 14 = 1.14; 16 ÷ 15 = 1.06; 16 ÷ 16 = 1

The factors of 16 are**1, 2, 4, 8** and **16**

The factors of 16 are

10.

For the whole number given below, find the right answer that lists all of the number’s factors.

13

13

1, 13

1, 3, 13

1, 3, 6, 13

1, 6, 13

13 ÷ 1 = 13; 13 ÷ 2 = 6.5; 13 ÷ 3 = 4.33; 13 ÷ 4 = 3.25; 13 ÷ 5 = 2.6; 13 ÷ 6 = 2.16; 13 ÷ 7 = 1.85; 13 ÷ 8 = 1.62; 13 ÷ 9 = 1.44; 13 ÷ 10 = 1.3; 13 ÷ 11 = 1.18; 13 ÷ 12 = 1.08; 13 ÷ 13 = 1

The factors of 13 are**1** and **13**

The factors of 13 are

The factors of 21 are

1, 3, 7and21