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1 Integers
1.1 Factors, multiples and primes
Exercise 1.1
E
Key words
Focus factor tree
highest common
1 a Draw a factor tree for 250 that starts with 2 × 125. factor (HCF)
b Can you draw a different factor tree for 250 that starts with
PL 2
3
c
a
2 × 125? Give a reason for your answer.
Draw a factor tree for 250 that starts with 25 × 10.
d Write 250 as a product of its prime factors.
Draw a factor tree for 300.
b Draw a different factor tree for 300.
c
a
Write 300 as a product of prime numbers.
Write as a product of prime numbers
i 6 ii 30 iii 210
lowest common
multiple (LCM)
prime factor
M
b What is the next number in this sequence? Why?
4 Work out
a 2×3×7 b 2 2 × 32 × 7 2 c 23 × 33 × 73
5 a Draw a factor tree for 8712.
b Write 8712 as a product of prime numbers.
SA
6 Write each of these numbers as a product of its prime factors.
a 96 b 97 c 98 d 99
Practice
7 Write as a product of prime numbers
a 70 b 702 c 703
8 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
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 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.
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
E
a 60 and 72 b 60 and 75 c 72 and 75
11 a Write 104 as a product of its prime factors.
b Write 130 as a product of its prime factors.
c Find the HCF of 104 and 130.
PL d Find the LCM of 104 and 130.
12 a Write 135 as a product of prime numbers.
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.
Challenge
M
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.
SA
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.
