Define the term integer .

Integers are whole numbers . They can be positive, negative or zero.

Define a factor of a number.

A factor of a number is a positive integer that divides exactly into the number.

Define a multiple of a number.

A multiple of a number is a positive integer that can be made by multiplying the number by another integer.

Define a prime number .

A prime number is a positive integer which has exactly two factors , itself and 1.

True or False? 1 is a prime number.

False. 1 is not a prime number, as it only has one factor .

What is the only even prime number ?

2 is the only even prime number.

What are the first ten prime numbers ?

The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

What are the first twelve square numbers ?

The first twelve square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

What are the first five cube numbers ?

The first five cube numbers are: 1, 8, 27, 64, 125.

True or False? Every number has at least two factors, itself and 1.

False. The number 1 has only one factor. Every other integer has at least two factors.

What type of numbers have an odd number of factors ?

Square numbers have an odd number of factors.

True or False? Any positive integer has an infinite number of multiples .

True. Any positive integer has an infinite number of multiples.

What are prime factors ?

Prime factors of a number are the prime numbers which are factors of the number.

Define the term highest common factor (HCF) of two numbers.

The highest common factor (HCF) is the largest positive integer that divides into both numbers exactly .

Define the term common factor .

A common factor of two numbers is a positive integer that both numbers can be divided by exactly .

What number is always a common factor of any two positive integers?

1 is always a common factor of any two numbers.

How can you find the HCF of two numbers?

To find the HCF, write each number as a product of its prime factors , find the common prime factors , and multiply them together.

Define the term lowest common multiple (LCM) of two numbers.

The lowest common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers .

Define the term common multiple .

A common multiple of two numbers is a number that appears in both of their times tables .

True or False? The product of two numbers is always the lowest common multiple.

False. The product of two numbers is always a common multiple , however it is not always the smallest .

How can you find the LCM of two numbers?

To find the LCM , write each number as a product of its prime factors , find the prime factors of the first number that are not prime factors of the second number and multiply the first number by these extra prime factors.

True or False? Any pair of numbers has a finite number of common factors .

True. Any pair of numbers will always have a finite number of common factors.

True or False? Any pair of numbers has a finite number of common multiples .

False. Any pair of numbers will always have an infinite number of common multiples. Once you have found a common multiple, you can multiply that by any positive integer to find another common multiple.

IGCSEMaths A: HigherEdexcelFlashcards

Prime Factors, HCF & LCM (Edexcel IGCSE Maths A)

Flashcards

1/26

FrontTypes of Number
Define the term integer.

Enjoying Flashcards?
Tell us what you think

Cards in this collection (26)

Define the term integer.
Integers are whole numbers. They can be positive, negative or zero.
Define a factor of a number.
A factor of a number is a positive integer that divides exactly into the number.
Define a multiple of a number.
A multiple of a number is a positive integer that can be made by multiplying the number by another integer.
Define a prime number.
A prime number is a positive integer which has exactly two factors, itself and 1.
True or False?
1 is a prime number.
False.
1 is not a prime number, as it only has one factor.
What is the only even prime number?
2 is the only even prime number.
What are the first ten prime numbers?
The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
What are the first twelve square numbers?
The first twelve square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
What are the first five cube numbers?
The first five cube numbers are: 1, 8, 27, 64, 125.
True or False?
Every number has at least two factors, itself and 1.
False.
The number 1 has only one factor. Every other integer has at least two factors.
What type of numbers have an odd number of factors?
Square numbers have an odd number of factors.
True or False?
Any positive integer has an infinite number of multiples.
True.
Any positive integer has an infinite number of multiples.
What are prime factors?
Prime factors of a number are the prime numbers which are factors of the number.
What is Prime Factor Decomposition?
Prime Factor Decomposition (or Prime Factorisation) is the process of breaking a number up into pairs of factors, then breaking those factors down in the same way until you are left with only prime factors.
E.g.
$\begin{array}{rcl} 72 & = & 8 \times 9 \\ = & (2 \times 4) \times (3 \times 3) \\ = & 2 \times 2 \times 2 \times 3 \times 3 \end{array}$
How do I write a number as a Product of Prime Factors?
A Product of Prime Factors can be found using Prime Factor Decomposition then writing the prime factors of a number multiplied together
E.g. $36$ written as a product of prime factors is $2 \times 2 \times 3 \times 3$ or $2^{2} \times 3^{2}$ .
True or False?
$500$ can be written as a product of prime factors in the form $2 \times 2 \times 5 \times 5 \times 5$ .
True.
The prime factorisation of $500 = 2 \times 2 \times 5 \times 5 \times 5$ .
You may be asked to give your answer in the form $2^{2} \times 5^{3}$ .
Define the term highest common factor (HCF) of two numbers.
The highest common factor (HCF) is the largest positive integer that divides into both numbers exactly.
Define the term common factor.
A common factor of two numbers is a positive integer that both numbers can be divided by exactly.
What number is always a common factor of any two positive integers?
1 is always a common factor of any two numbers.
How can you find the HCF of two numbers?
To find the HCF, write each number as a product of its prime factors, find the common prime factors, and multiply them together.
Define the term lowest common multiple (LCM) of two numbers.
The lowest common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.
Define the term common multiple.
A common multiple of two numbers is a number that appears in both of their times tables.
True or False?
The product of two numbers is always the lowest common multiple.
False.
The product of two numbers is always a common multiple, however it is not always the smallest.
How can you find the LCM of two numbers?
To find the LCM, write each number as a product of its prime factors, find the prime factors of the first number that are not prime factors of the second number and multiply the first number by these extra prime factors.
True or False?
Any pair of numbers has a finite number of common factors.
True.
Any pair of numbers will always have a finite number of common factors.
True or False?
Any pair of numbers has a finite number of common multiples.
False.
Any pair of numbers will always have an infinite number of common multiples. Once you have found a common multiple, you can multiply that by any positive integer to find another common multiple.

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability