Factors, Powers And Standard Form Worksheet Page 13
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21Using prime factors to find the HCF
• Write each number as the product of prime factors.
If a prime number is only
• If a prime number is in both lists, circle the lowest power.
in one of the lists you can’t
include it in your HCF.
• Multiply these to fi nd the HCF.
Using prime factors to find the LCM
• Write each number as the product of prime factors.
• Circle the highest power of each prime number.
• Multiply these to fi nd the LCM.
Example 9
C
Work out
a
the HCF of 180 and 168
b
the LCM of 24 and 60.
The prime numbers in both lists
a 180 5 2
2
3 3
2
3 5
are 2 and 3. The lowest power of 2
2
1
is 2
. The lowest power of 3 is 3
.
168 5 2
3
3 3 3 7
The HCF of 180 and 168 is 2
2
3 3 5 12.
b 24 5 2
3
3 3
You only need to circle the highest power of 2.
60 5 2
2
3 3 3 5
3 is a factor of 24 and
60. You only need to
The LCM of 24 and 60 is 2
3
3 3 3 5 5 120.
circle it once.
Exercise 10I
C
1
a
Write 90 as a product of prime factors.
b
Write 165 as a product of prime factors.
c
Find the HCF of 90 and 165.
2
a
Write 42 as a product of prime factors.
b
Write 30 as a product of prime factors.
c
Find the LCM of 42 and 30.
3
Work out the highest common factor of each pair of numbers.
a
b
c
32 and 56
80 and 72
27 and 45
d
100 and 75
e
48 and 64
f
60 and 160
4
Work out the largest whole number that will divide exactly into 264 and 150.
5
Work out the lowest common multiple of each pair of numbers.
a
b
c
18 and 20
6 and 32
27 and 15
d
9 and 75
e
60 and 80
f
14 and 21
6
Work out the smallest number that is a multiple of 90 and a multiple of 105.
170
Factors, powers and standard form
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