Download Prime and Composite Numbers (Skill sheet)

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Skillsheet
Prime and composite numbers
Factors
The factors of a number are those whole numbers that divide into that number exactly.
Example 1
List the factors of 10.
Solution
The numbers that divide into 10 exactly are 2, 5, 10 and 1. For example, 10 2 ¼ 5 and 10 1 ¼ 10.
The factors of 10 are 1, 2, 5 and 10.
Note that the factors of a number occur in ‘product pairs’. For the number 10 in Example 1, we know that 2 5 ¼ 10, and 1 10 ¼ 10, so 2, 5, 1, 10 are the factors. Using product pairs is an effective way of finding the
factors of larger numbers.
Example 2
List the factors of 56.
Solution
Product pairs that give 56 are: 1 56, 2 28, 4 14, 7 8.
So the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
If we list product pairs in order, as the first terms increase (1 56, 2 28, 4 14, 7 8), the second terms
decrease (1 56, 2 28, 4 14, 7 8). Using this property, we can stop testing for factors once we reach
the ‘halfway mark’. In Example 2, we can stop testing numbers after 7 because 8, which appears as a second
term, has already been found. Now we have found all of the factors of the number.
Example 3
List the factors of 88.
Solution
Product pairs that give 88: 1 88, 2 44, 4 22, 8 11. We can stop testing for factors after 10 because
11, which appears as a second term, has already been found. The factors of 88 are 1, 2, 4, 8, 11, 22, 44 and 56.
Notice that every number greater than one has at least two factors, 1 and itself.
Prime numbers
Numbers that have only two factors (1 and itself) are called prime numbers. For example, 3, 7 and 11 are
prime.
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The factors of 3 are 1 and 3.
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The factors of 7 are 1 and 7.
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The factors of 11 are 1 and 11.
No other numbers divide into these prime numbers.
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10017
Number and Algebra: Number and place value
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Composite numbers
Numbers that have more than two factors are called composite numbers. For example, 4, 14 and 15 are
composite.
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The factors of 4 are 1, 2 and 4.
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The factors of 14 are 1, 2, 7 and 14.
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The factors of 15 are 1, 3, 5 and 15.
The only whole number that is neither prime nor composite is 1. It has only one factor, itself.
Example 4
Determine whether each number is prime or composite.
a 18
b 23
c 31
d 51
Solution
a 18 is divisible by 2, so 2 is a factor. This means that 18 has more than 2 factors (1 and 18). So 18 is
composite.
b 23 is not divisible by any number other than 1 and itself. So 23 is prime.
c 31 is not divisible by any number other than 1 and itself. So 31 is prime.
d 51 is divisible by 3 (the sum of its digits is 6, which is divisible by 3), so 3 is a factor.
This means that 51 has more than 2 factors (1 and 51). So 51 is composite.
Exercises
1 Find the factors of each number.
a 8
b 13
c 25
d 12
e 40
f 37
g 36
h 70
i 26
j 29
k 54
l 101
2 Which of the numbers in Question 1 are prime?
3 Determine whether each number is prime or composite.
a 96
b 22
c 71
d 59
e 49
f 65
g 83
h 147
4 List the 10 prime numbers between 1 and 30.
5 List the 16 composite numbers from 30 to 50 (inclusive).
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10017
Number and Algebra: Number and place value
www.nelsonnet.com.au
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Answers
1 a 1, 2, 4, 8
b 1, 13
c 1, 5, 25
d 1, 2, 3, 4, 6, 12
e 1, 2, 4, 5, 8, 10, 20, 40
f 1, 37
g 1, 2, 3, 4, 6, 9, 12, 18, 36
h 1, 2, 5, 7, 10, 14, 35, 70
i 1, 2, 13, 26
j 1, 29
k 1, 2, 3, 6, 9, 18, 27, 54
3 a composite
b composite
c prime
d prime
e composite
f composite
g prime
h composite
l 1, 101
2 13, 37, 29, 101
4 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
5 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50.
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10017
Number and Algebra: Number and place value
www.nelsonnet.com.au