Types of Number, Prime Factors, HCF & LCM (Edexcel GCSE Maths: Foundation): Exam Questions

Here is a whole list of numbers from 2 to 15

2        3        4        5        6        7        8        9        10        11        12        13        14        15

From the list write down a cube number.

From the list write down all the factors of 24.

Write down two prime numbers that have a sum of 40.

Ellis says

"There are more prime numbers between 40 and 50 than there are between 30 and 40"

Is Ellis correct?

You must show how you get your answer.

From this list, write down

i) a factor of 54,

[1]

ii) a multiple of 19,

[1]

iii) a prime number.

[1]

Write down

i) all the factors of 21,

[2]

ii) a prime number between 40 and 50.

[1]

A road has 349 houses on it numbered from 1 to 349.
The diagram shows some of these houses.
The houses on the West side of the road have odd numbers.
The houses on the East side have even numbers.

Write down the numbers in this list that are on the West side.

On the East side, how many houses are there between the house numbered 168 and the house numbered 184?

How many houses on the road have a house number that is a multiple of 39?

Write down

i) all the factors of 18,

[2]

ii) a square number between 30 and 50,

[1]

iii) a prime number between 90 and 100.

[1]

Find the first even multiple of seven that is greater than 100.

From the list, write down the irrational number.

Here is a list of numbers.

From this list, write down a prime number.

From this list, write down an irrational number.

Using the integers from 60 to 75 only, find

i) a multiple of 17,

[1]

ii) the prime numbers.

[2]

Write down the reciprocal of 7.

From this list of numbers, write down a multiple of 8.

From this list of numbers, write down a square number.

From this list of numbers, write down a prime number.

Here is a list of numbers.

From this list, write down a cube number.

From this list, write down a prime number.

From the list of numbers, write down a multiple of 7.

From the list of numbers, write down a cube number.

From the list of numbers, write down a prime number.

Write 825 as the product of its prime factors.

Find the lowest common multiple (LCM) of 48 and 60.

Write 195 as a product of its prime factors.

i) Write 60 as a product of its prime factors.

[2]

ii) Find the lowest common multiple (LCM) of 36 and 60.

[2]

Write 432 as the product of its prime factors.

Find the highest common factor (HCF) of 24 and 108.

Find the highest common factor (HCF) of 90 and 48.

Find the lowest common multiple (LCM) of 28 and 35.

Write down the value of .

Write down the value of 

Write down a prime number that is also a factor of 56.

Aziz chooses a prime number and a square number.

He adds together his two numbers.
The result is a cube number that is smaller than 30.

Find two numbers that Aziz could have written down.

Using numbers from 55 to 85, write down

i) a multiple of 23,

[1]

ii) a factor of 120,

[1]

iii) a common multiple of 8 and 12,

[1]

iv) a number that is both square and odd,

[1]

v) a number that has exactly 2 factors.

[1]

The diagram shows five number cards.

Put two cards side by side to show

i) a two-digit number that is a multiple of 7,

[1]

ii) a two-digit square number,

[1]

iii) a two-digit cube number,

[1]

iv) a two-digit prime number.

[1]

Write down a common factor of 16 and 72 that is greater than 2.

Show that there is not a square number between 50 and 60.

Write down a prime number between 50 and 60.

Find

i) the smallest multiple of 7 that is greater than 100,

[1]

ii) the largest cube number that is less than 100,

[1]

iii) the six factors of 45,

[2]

At a bus stop

• a red bus arrives every 18 minutes

and

• a blue bus arrives every 24 minutes.

At 1047 a red bus and a blue bus arrive.

Find the next time when a red bus and a blue bus arrive together.

Find the highest common factor (HCF) of 126 and 180.

i) Find the highest common factor (HCF) of 36 and 90.

[2]

ii) Find the lowest common multiple (LCM) of 36 and 90.

[2]

Gerry and Alain run around a running track.

To run around the track once

• Gerry always takes 90 seconds

• Alain always takes 105 seconds.

They start together at the same point.

After how many minutes are they next together at that point?

........................................ min

i) Find the highest common factor (HCF) of 28 and 98.

[2]

ii) Find the lowest common multiple (LCM) of 28 and 98.

[2]

Talan completes one lap of a track every 80 seconds.

i) Work out how many laps he can complete in one hour.

[2]

ii) Naima completes one lap of the same track every 88 seconds. Talan and Naima start running from point  on the track at the same time. They each complete a number of laps of the track.

Work out the smallest number of laps they each complete before they are both at point  again at the same time.

Talan completes ................. laps and Naima completes ................. laps. [3]