● 2 1.1 Understanding prime factors, LCM and HCF 61A 1 Write down all the factors of each of the following numbers. a 12 ...................................................................... b 30 ...................................................................... c 36 ...................................................................... d 40 ...................................................................... 2 Use this factor tree to write 54 as a product of its prime factors. ..................................................................................................... ..................................................................................................... ..................................................................................................... 3 Complete the following factor trees. a b c 4 Write each of the following numbers as the product of its prime factors. How can factor trees be drawn before working through to find out how many factors there are? a 24 ...................................................................... b 40 ...................................................................... c 50 ...................................................................... d 72 ...................................................................... e 100 ...................................................................... 5 a Write out all the factors of i 4 ...................................................................... ii 6 ...................................................................... iii 10 ...................................................................... iv 16 ...................................................................... v 20 ...................................................................... b Use part a to help you write down the highest common factor (HCF) of i 4 and 10 ...................................................................... ii 6 and 16 ...................................................................... iii 4 and 20 ...................................................................... iv 16 and 20 ...................................................................... v 10 and 16 ...................................................................... Write down the factors in pairs. 2 3 3 3 6 9 54 21 42 10 70 21 84 Remember to draw factor trees first. Factors are numbers that go exactly into the given number. Guided practice worksheet D C Questions are targeted at the grades indicated
Transcript
�2 1.1 Understanding prime factors, LCM and HCF
61A
1 Write down all the factors of each of the following numbers.
a 12 ...................................................................... b 30 ......................................................................
c 36 ...................................................................... d 40 ......................................................................
2 Use this factor tree to write 54 as a product of its prime factors.
4 Write each of the following numbers as the product of its prime factors. How can factor trees be drawn before working through to � nd out how many factors there are?
a 24 ...................................................................... b 40 ......................................................................
c 50 ...................................................................... d 72 ......................................................................
e 100 ......................................................................
5 a Write out all the factors of
i 4 ...................................................................... ii 6 ......................................................................
iii 10 ...................................................................... iv 16 ......................................................................
v 20 ......................................................................
b Use part a to help you write down the highest common factor (HCF) of
i 4 and 10 ...................................................................... ii 6 and 16 ......................................................................
iii 4 and 20 ...................................................................... iv 16 and 20 ......................................................................
v 10 and 16 ......................................................................
Write down the factors in pairs.
2 33 3
6 9
54
21
42
10
70
21
84
Remember to draw factor trees � rst.
Factors are numbers that go exactly into the given number.
Guided practice worksheet
D
C
Questions are targeted at the grades indicated
�2 1.1 Understanding prime factors, LCM and HCF
61B
Guided practice worksheet
6 a Write out the first ten multiples of
i 4 ...................................................................... ii 6 ......................................................................
b Write out the first six multiples of
i 10 ...................................................................... ii 16 ......................................................................
iii 20 ......................................................................
c Use your answers to parts a and b to help you write down the lowest common multiple (LCM) of
i 4 and 6 ...................................................................... ii 6 and 10 ......................................................................
iii 4 and 16 ...................................................................... iv 16 and 20 ......................................................................
v 6 and 20 ......................................................................
7 a Use your answers to question 3 to write 42, 70 and 84 as products of their prime factors.
i 42 ............................................................................................................................................................................................................................
ii 70 ............................................................................................................................................................................................................................
iii 84 ...........................................................................................................................................................................................................................
8 Find the HCF and LCM of the following pairs of numbers.
a 60 and 84 .................................................................................... b 70 and 105 ..................................................................................
c 72 and 96 ..................................................................................... d 84 and 96 .....................................................................................
Multiples are the numbers in the times table of the given number.
C
�2 1.2 Understanding squares and cubes
63A
1 Work out
a 32 ......................................................... b 42 ......................................................... c 52 .........................................................
d 72 ......................................................... e 102 .........................................................
2 Lizzy says that to work out 62 you do 6 × 2 so the answer is 12. Lizzy is wrong. Explain why.
a 23 ......................................................... b 33 ......................................................... c 43 .........................................................
d 53 ......................................................... e 103 .........................................................
c 4 .................................................................................................. d 49 ................................................................................................
a (–2)2 ............................................................................................. b (–2)3 ...............................................................................................
c (–6)2 .............................................................................................. d (–8)2 ..............................................................................................
a 52 + 22 .................................................................................. b 82 – 32 .................................................................................
e 53 – 13 ................................................................................... f 43 ÷ 82 ................................................................................
a 52 + 22 .......................................................................................... b (5 + 2)2 .......................................................................................
c 3 × 42 ......................................................................................... d 100 – 82 .......................................................................................
a 43 ..................................................................................................... b 92 ....................................................................................................
c 26 ..................................................................................................... d 104 ..................................................................................................
e 35 .....................................................................................................
2 Write in index form
a 2 × 2 × 2 × 2 × 2 ....................................................................... b 6 × 6 × 6 ......................................................................................
c 8 × 8 × 8 × 8 × 8 × 8 × 8 ........................................................ d 17 × 17 .........................................................................................
3 Write as a power of 7
a 75 × 73 ............................................................................................ b 72 × 78 ...........................................................................................
c 73 × 7 .............................................................................................. d 76 × 76 ...........................................................................................
a 56 ÷ 52 ............................................................................................ b 59 ÷ 56 ...........................................................................................
c 512 ÷ 54 ........................................................................................... d 57 ÷ 5 ............................................................................................
a 39 × 32 ............................................................................................ b 37 ÷ 33 ............................................................................................
c 310 ÷ 34 ........................................................................................... d 3 × 34 ............................................................................................
a (62)4 ................................................................................................ b (64)3 ...............................................................................................
c (68)5 ................................................................................................. d (69)3 ...............................................................................................
a 73 × 75 ............................................................................................ b (94)2 ................................................................................................
