CAIE IGCSE Mathematics Extended E1.1 Types of Number Questions

Practise working with factors, multiples and prime factor forms to find HCFs, LCMs and number products accurately.

Exam points

write numbers as products of prime factors using factor trees, tables or lists
use prime factors or lists to find the HCF or LCM of two numbers
recognise factors, multiples and square-number products from integer properties

Covered syllabus points

E1.1.1 Identify and use: • natural numbers • integers (positive, zero and

[Maximum number: 2]

Find the highest common factor (HCF) of 36 and 54.

B1 for answer 2, 3, 6 or 9;
or M1 for $2\times3^2$ oe;
or for correct factor trees/tables

[Maximum number: 2]

$k=2\times3^2\times p^3$
where p is a prime number greater than 3.
Write $6k^2$ as a product of prime factors in terms of p.

$2^3\times3^5\times p^6$
final answer

B1 for two parts correct, or $2\times3\times2\times3^2\times p^3\times2\times3^2\times p^3$ , or $1944p^6$ , or $k^2=2^2\times3^4\times p^6$

[Maximum number: 4]

$13 \quad M=2^{7} \times 3^{3} \times 5^{2}$

(a)

Write 14 M as a product of its prime factors.

Give your answer in index form.

[ 2 ]

$2^8\times3^3\times5^2\times7$ cao

M1 for $14=2\times7$ soi

(b)

R is an integer.
$\frac{M}{R}$ is a cube number.
Find the smallest possible value of R.

[ 2 ]

50
or -86400

M1 for $2^3\times3^3$ or $2^6\times3^3$ oe or $2^4\times5^2$ or $2\times5^2$ oe
or SC1 for answers -50, [-]400, [-]1350, [-]3200, [-]10800, 86400 oe

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (b)