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1
Integers
Exercise 1.1
Focus
2
3
4
SA
5
Draw a factor tree for 250 that starts with 2 × 125.
Can you draw a different factor tree for 250 that starts with
2 × 125? Give a reason for your answer.
c
Draw a factor tree for 250 that starts with 25 × 10.
d Write 250 as a product of its prime factors.
a
Draw a factor tree for 300.
b Draw a different factor tree for 300.
c
Write 300 as a product of prime numbers.
a
Write as a product of prime numbers
i
6
ii
30
iii 210
b What is the next number in this sequence? Why?
Work out
a
2×3×7
b 22 × 32 × 72
c
23 × 33 × 73
a
Draw a factor tree for 8712.
b Write 8712 as a product of prime numbers.
Write each of these numbers as a product of its prime factors.
a
96
b 97
c
98
d 99
a
b
M
1
PL
E
1.1 Factors, multiples and primes
6
Key words
factor tree
highest common
factor (HCF)
lowest common
multiple (LCM)
prime factor
210
10
5
8
Write as a product of prime numbers
a
70
b 702
c
703
a
Write each square number as a product of its prime factors.
i
9
ii
36
iii 81
iv 144
v
225
vi 576
vii 625
viii 2401
2
7
3
96
12
8
Practice
7
21
4
2
2
4
3
2
2
2
7 to publication.
Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior
We are working with Cambridge Assessment International Education towards endorsement of this title.
1 Integers
b
13
8
4
2
2
2
M
Challenge
104
PL
E
When a square number is written as a product of prime numbers,
what can you say about the factors?
c
176 400 = 24 × 32 × 52 × 72
Use this fact to show that 176 400 is a square number.
A:
9
315 = 32 × 5 × 7
252 = 22 × 32 × 7
660 = 22 × 3 × 5 × 11
Use these facts to find the highest common factor of
a
315 and 252
b 315 and 660
c
252 and 660
10 60 = 22 × 3 × 5
72 = 23 × 32
75 = 3 × 52
Use these facts to find the lowest common multiple of
a
60 and 72
b 60 and 75
c
72 and 75
11 a
Write 104 as a product of its prime factors.
130
b Write 130 as a product of its prime factors.
c
Find the HCF of 104 and 130.
13
10
d Find the LCM of 104 and 130.
12 a
Write 135 as a product of prime numbers.
5
2
b Write 180 as a product of prime numbers.
c
Find the HCF of 135 and 180.
d Find the LCM of 135 and 180.
SA
13 a
Write 343 as a product of prime numbers.
b Write 546 as a product of prime numbers.
c
Find the HCF of 343 and 546.
d Find the LCM of 343 and 546.
14 Find the LCM of 42 and 90.
15 a
Find the HCF of 168 and 264.
b Find the LCM of 168 and 264.
16 a
Show that the LCM of 48 and 25 is 1.
b Find the HCF of 48 and 25.
17 The HCF of two numbers is 6. The LCM of the two numbers is 72.
What are the two numbers?
8
Original material
© Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.