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# Highest Common Factors

This Math quiz is called 'Highest 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.

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A factor is a number that can be evenly divided into other whole numbers without having a remainder left over. For example, 9 is a common factor of 1, 3 and 9. Fractions and decimals are not found in common factors making finding common factors rather easy.

1.
For the whole numbers given below, find the common highest factor.

8 and 16
4
8
6
2
8 ÷ 1 = 8; 8 ÷ 2 = 4; 8 ÷ 3 = 2.66; 8 ÷ 4 = 2; 8 ÷ 5 = 1.6; 8 ÷ 6 = 1.33; 8 ÷ 7 = 1.14; 8 ÷ 8 = 1

16 ÷ 1 = 16; 16 ÷ 2 = 8; 16 ÷ 3 = 5.33; 16 ÷ 4 = 4; 16 ÷ 5 = 3.2; 16 ÷ 6 = 2.66; 16 ÷ 7 = 2.57; 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 8 are 1, 2, 4 and 8. The factors of 16 are 1, 2, 4, 8 and 16. The factors that can be found in both 8 and 16 include the numbers 1, 2, 4 and 8. 8 is, therefore, the highest common factor so Answer (b) is the correct answer
2.
For the whole numbers given below, find the common highest factor.

19 and 42
1
4
6
8
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

42 ÷ 1 = 42; 42 ÷ 2 = 21; 42 ÷ 3 = 14; 42 ÷ 4 = 10.5; 42 ÷ 5 = 8.4; 42 ÷ 6 = 7; 42 ÷ 7 = 6; 42 ÷ 8 = 5.25; 42 ÷ 9 = 4.66; 42 ÷ 10 = 4.2; 42 ÷ 11 = 3.81; 42 ÷ 12 = 3.5; 42 ÷ 13 = 3.23; 42 ÷ 14 = 3; 42 ÷ 15 = 2.8; 42 ÷ 16 = 2.62; 42 ÷ 17 = 2.47; 42 ÷ 18 = 2.33; 42 ÷ 19 = 2.21; 42 ÷ 20 = 2.1; 42 ÷ 21 = 2; 42 ÷ 22 = 1.90; 42 ÷ 23 = 1.82; 42 ÷ 24 = 1.75; 42 ÷ 25 = 1.68; 42 ÷ 26 = 1.61; 42 ÷ 27 = 1.55; 42 ÷ 28 = 1.5; 42 ÷ 29 = 1.44; 42 ÷ 30 = 1.4; 42 ÷ 31 = 1.35; 42 ÷ 32 = 1.31; 42 ÷ 33 = 1.27; 42 ÷ 34 = 1.23; 42 ÷ 35 = 1.2; 42 ÷ 36 = 1.16; 42 ÷ 37 = 1.13; 42 ÷ 38 = 1.1; 42 ÷ 39 = 1.07; 42 ÷ 40 = 1.05; 42 ÷ 41 = 1.02; 42 ÷ 42 = 1

The factors of 19 are 1 and 19. The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. The factors that can be found in both 19 and 42 include only the number 1. 1 is, therefore, the highest common factor so Answer (a) is the correct answer
3.
For the whole numbers given below, find the common highest factor.

13 and 26
1
3
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

26 ÷ 1 = 26; 26 ÷ 2 = 13; 26 ÷ 3 = 8.66; 26 ÷ 4 = 6.5; 26 ÷ 5 = 5.2; 26 ÷ 6 = 4.33; 26 ÷ 7 = 3.71; 26 ÷ 8 = 3.25; 26 ÷ 9 = 2.88; 26 ÷ 10 = 2.6; 26 ÷ 11 = 2.36; 26 ÷ 12 = 2.16; 26 ÷ 13 = 2; 26 ÷ 14 = 1.85; 26 ÷ 15 = 1.73; 26 ÷ 16 = 1.62; 26 ÷ 17 = 1.52; 26 ÷ 18 = 1.44; 26 ÷ 19 = 1.36; 26 ÷ 20 = 1.3; 26 ÷ 21 = 1.23; 26 ÷ 22 = 1.18; 26 ÷ 23 = 1.13; 26 ÷ 24 = 1.08; 26 ÷ 25 = 1.04; 26 ÷ 26 = 1

The factors of 13 are 1 and 13. The factors of 26 are 1, 2, 13 and 26. The factors that can be found in both 13 and 26 include the numbers 1 and 13. 13 is, therefore, the highest common factor so Answer (d) is the correct answer
4.
For the whole numbers given below, find the common highest factor.

9 and 18
9
3
1
4
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

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 9 are 1, 3 and 9. The factors of 18 are 1, 2, 3, 6, 9 and 18. The factors that can be found in both 9 and 18 include the numbers 1, 3 and 9. 9 is, therefore, the highest common factor so Answer (a) is the correct answer
5.
For the whole numbers given below, find the common highest factor.

11 and 23
3
5
7
1
11 ÷ 1 = 11; 11 ÷ 2 = 5.5; 11 ÷ 3 = 3.66; 11 ÷ 4 = 2.75; 11 ÷ 5 = 2.2; 11 ÷ 6 = 1.83; 11 ÷ 7 = 1.57; 11 ÷ 8 = 1.37; 11 ÷ 9 = 1.22; 11 ÷ 10 = 1.1; 11 ÷ 11 = 1

23 ÷ 1 = 23; 23 ÷ 2 = 11.5; 23 ÷ 3 = 7.66; 23 ÷ 4 = 5.75; 23 ÷ 5 = 4.6; 23 ÷ 6 = 3.83; 23 ÷ 7 = 3.28; 23 ÷ 8 = 2.87; 23 ÷ 9 = 2.55; 23 ÷ 10 = 2.3; 23 ÷ 11 = 2.09; 23 ÷ 12 = 1.91; 23 ÷ 13 = 1.76; 23 ÷ 14 = 1.64; 23 ÷ 15 = 1.53; 23 ÷ 16 = 1.43; 23 ÷ 17 = 1.35; 23 ÷ 18 = 1.27; 23 ÷ 19 = 1.21; 23 ÷ 20 = 1.15; 23 ÷ 21 = 1.09; 23 ÷ 22 = 1.04; 23 ÷ 23 = 1

The factors of 11 are 1 and 11. The factors of 23 are 1 and 23. The factors that can be found in both 11 and 23 include only the number 1. 1 is, therefore, the highest common factor so Answer (d) is the correct answer
6.
For the whole numbers given below, find the common highest factor.

15 and 20
1
4
5
6
15 ÷ 1 = 15; 15 ÷ 2 = 7.5; 15 ÷ 3 = 5; 15 ÷ 4 = 3.75; 15 ÷ 5 = 3; 15 ÷ 6 = 2.5; 15 ÷ 7 = 2.14; 15 ÷ 8 = 1.87; 15 ÷ 9 = 1.66; 15 ÷ 10 = 1.5; 15 ÷ 11 = 1.36; 15 ÷ 12 = 1.25; 15 ÷ 13 = 1.15; 15 ÷ 14 = 1.07; 15 ÷ 15 = 1

20 ÷ 1 = 20; 20 ÷ 2 = 10; 20 ÷ 3 = 6.66; 20 ÷ 4 = 5; 20 ÷ 5 = 4; 20 ÷ 6 = 3.33; 20 ÷ 7 = 2.85; 20 ÷ 8 = 2.5; 20 ÷ 9 = 2.22; 20 ÷ 10 = 2; 20 ÷ 11 = 1.81; 20 ÷ 12 = 1.66; 20 ÷ 13 = 1.53; 20 ÷ 14 = 1.42; 20 ÷ 15 = 1.33; 20 ÷ 16 = 1.25; 20 ÷ 17 = 1.17; 20 ÷ 18 = 1.11; 20 ÷ 19 = 1.05; 20 ÷ 20 = 1

The factors of 15 are 1, 3, 5 and 15. The factors of 20 are 1, 2, 4, 5, 10 and 20. The factors that can be found in both 15 and 20 include the numbers 1 and 5. 5 is, therefore, the highest common factor so Answer (b) is the correct answer
7.
For the whole numbers given below, find the common highest factor.

24 and 32
8
12
16
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

32 ÷ 1 = 32; 32 ÷ 2 = 16; 32 ÷ 3 = 10.66; 32 ÷ 4 = 8 ; 32 ÷ 5 = 6.4; 32 ÷ 6 = 5.33; 32 ÷ 7 = 4.57; 32 ÷ 8 = 4; 32 ÷ 9 = 3.55; 32 ÷ 10 = 3.2; 32 ÷ 11 = 2.90; 32 ÷ 12 = 2.66; 32 ÷ 13 = 2.46; 32 ÷ 14 = 2.28; 32 ÷ 15 = 2.13; 32 ÷ 16 = 2; 32 ÷ 17 = 1.88; 32 ÷ 18 = 1.77; 32 ÷ 19 = 1.68; 32 ÷ 20 = 1.6; 32 ÷ 21 = 1.52; 32 ÷ 22 = 1.45; 32 ÷ 23 = 1.39; 32 ÷ 24 = 1.33; 32 ÷ 25 = 1.28; 32 ÷ 26 = 1.23; 32 ÷ 27 = 1.18; 32 ÷ 28 = 1.14; 32 ÷ 29 = 1.1; 32 ÷ 30 = 1.06; 32 ÷ 31 = 1.03; 32 ÷ 32 = 1

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The factors of 32 are 1, 2, 4, 8, 16 and 32. The factors that can be found in both 24 and 32 include the numbers 1, 2, 4 and 8. 8 is, therefore, the highest common factor so Answer (a) is the correct answer
8.
For the whole numbers given below, find the common highest factor.

14 and 21
1
3
7
14
14 ÷ 1 = 14; 14 ÷ 2 = 7; 14 ÷ 3 = 4.66; 14 ÷ 4 = 3.5; 14 ÷ 5 = 2.8; 14 ÷ 6 = 2.33; 14 ÷ 7 = 2; 14 ÷ 8 = 1.74; 14 ÷ 9 = 1.55; 14 ÷ 10 = 1.4; 14 ÷ 11 = 1.27; 14 ÷ 12 = 1.16; 14 ÷ 13 = 1.07; 14 ÷ 14 = 1

21 ÷ 1 = 21; 21 ÷ 2 = 10.5; 21 ÷ 3 = 7; 21 ÷ 4 = 5.25; 21 ÷ 5 = 4.2; 21 ÷ 6 = 3.5; 21 ÷ 7 = 3; 21 ÷ 8 = 2.62; 21 ÷ 9 = 2.33; 21 ÷ 10 = 2.1; 21 ÷ 11 = 1.90; 21 ÷ 12 = 1.75; 21 ÷ 13 = 1.61; 21 ÷ 14 = 1.5; 21 ÷ 15 = 1.4; 21 ÷ 16 = 1.31; 21 ÷ 17 = 1.23; 21 ÷ 18 = 1.16; 21 ÷ 19 = 1.10; 21 ÷ 20 = 1.05; 21 ÷ 21 = 1

The factors of 14 are 1, 2, 7 and 14. The factors of 21 are 1, 3, 7 and 31. The factors that can be found in both 14 and 21 include the numbers 1 and 7. 7 is, therefore, the highest common factor so Answer (c) is the correct answer
9.
For the whole numbers given below, find the common highest factor.

6 and 10
6
5
2
1
6 ÷ 1 = 6; 6 ÷ 2 = 3; 6 ÷ 3 = 2; 6 ÷ 4 = 1.5; 6 ÷ 5 = 1.2; 6 ÷ 6 = 1

10 ÷ 1 = 10; 10 ÷ 2 = 5; 10 ÷ 3 = 3.33; 10 ÷ 4 = 2.5; 10 ÷ 5 = 2; 10 ÷ 6 = 1.66; 10 ÷ 7 = 1.42; 10 ÷ 8 = 1.25; 10 ÷ 9 = 1.1; 10 ÷ 10 = 1

The factors of 6 are 1, 2, 3 and 6. The factors of 10 are 1, 2, 5 and 10. The factors that can be found in both 6 and 10 include the numbers 1 and 2. 2 is, therefore, the highest common factor so Answer (c) is the correct answer
10.
For the whole numbers given below, find the common highest factor.

16 and 36
3
4
6
8
16 ÷ 1 = 16; 16 ÷ 2 = 8; 16 ÷ 3 = 5.33; 16 ÷ 4 = 4; 16 ÷ 5 = 3.2; 16 ÷ 6 = 2.66; 16 ÷ 7 = 2.57; 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

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 16 are 1, 2, 4, 8 and 16. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The factors that can be found in both 16 and 36 include the numbers 1, 2 and 4. 4 is, therefore, the highest common factor so Answer (b) is the correct answer
Author:  Christine G. Broome