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 lowest common multiple (LCM) of 30 and 75.

150
B1 for answer $150k$
or M1 for prime factors of 30 or 75 seen, a list of multiples of both 30 and 75 with at least 3 of each, $\frac{30\times75}{15}$ oe, or answer $2\times3\times5^2$

[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: 6]

(a)

Write 70 as a product of its prime factors.

[ 2 ]

$2\times5\times7$ [=70]

B1 for 2, 5, 7

(b)

Find the highest common factor (HCF) of 70 and 112.

[ 2 ]

14

M1 for $[112=]2^4\times7$ oe
or for answer $2\times7$

(c)

Find the lowest common multiple (LCM) of $70 x^{4} y^{2}$ and $112 x^{3} y^{5}$ .

[ 2 ]

$560x^4y^5$

B1 for answer $kx^4y^5$ or for answer $560x^ay^b$
or for correct answer seen then spoiled

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Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (b)

Question (c)