3
a Express 36 as a product of its prime factors. b Write your answer to part a using index notation. c Use you answer to part b to write 18 and 72 as a product of their prime factors using index notation.
4
119 = 7 × 17 1192 = 14 161 1193 = 1 685 159 a Write 14 161 as a product of prime factors using index notation. b Write 1 685 159 as a product of prime factors using index notation. c Write 11910 as a product of prime factors using index notation.
5
A mathematician wants to donate a total of £18 to three charities so that they each receive a whole number of pounds and the amount given to each charity is a factor of 18. How much does he give to each charity?
6
The first three odd prime numbers are all factors of 105. Explain why this means that seven people can share £105 equally so that each receives an exact number of pounds.
Homework 1H 1
2
3
Find the LCM of each pair of numbers. a 5 and 7
b 3 and 8
c 6 and 9
d 10 and 12
e 10 and 15
f 12 and 16
g 16 and 24
h 15 and 35
Find the HCF of each pair of numbers. a 21 and 49
b 27 and 45
c 15 and 25
d 25 and 45
e 48 and 60
f 72 and 108
g 54 and 126
h 99 and 132
Write each of these as a single power of x. a x2 × x3
b x4 × x5
4
Find the HCF of 55 555 and 67 750.
5
Find the LCM of 144 and 162.
6
Nuts are sold in packs of 12.
c x6 × x
d x5 × x5
e x3 × x2 × x4
Bolts are sold in packs of 18. What is the least number of each pack that needs to be bought in order to have the same numbers of nuts and bolts?
7
The HCF of two numbers is 5. The LCM of the same two numbers is 150. What are the numbers?
1.5 Prime factors, LCM and HCF
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