What are factors and how do I find them?

Factors are numbers that divide another number exactly without leaving a remainder. To find the factors of a number, you can start by dividing the number by integers starting from 1 up to the number itself. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. This concept is fundamental in the Edexcel Lower Secondary Mathematics curriculum under the Number topic.

What are multiples and how are they different from factors?

Multiples of a number are the products you get when you multiply that number by integers. Unlike factors, which are limited, multiples are infinite. For example, the multiples of 3 include 3, 6, 9, 12, and so on. Understanding the difference between factors and multiples is crucial for mastering the Number subtopic in Edexcel Lower Secondary Mathematics.

How do I determine the greatest common factor (GCF) of two numbers?

The greatest common factor (GCF) is the largest number that is a factor of two or more numbers. To find the GCF, list the factors of each number and identify the largest factor they have in common. For instance, the GCF of 18 and 24 is 6. This concept is an important part of the Edexcel Lower Secondary Mathematics curriculum.

What is the least common multiple (LCM) and how do I find it?

The least common multiple (LCM) of two numbers is the smallest multiple that is common to both numbers. To find the LCM, list the multiples of each number and identify the smallest multiple they share. For example, the LCM of 4 and 5 is 20. This topic is covered under the Number section in Edexcel Lower Secondary Mathematics.

Why are factors and multiples important in Mathematics?

Factors and multiples are foundational concepts in Mathematics that help in understanding more complex topics such as fractions, ratios, and algebra. They are essential for problem-solving and are widely used in various mathematical operations. Mastery of these concepts is crucial for students following the Edexcel Lower Secondary Mathematics curriculum.

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NumberEdexcel Lower Secondary Mathematics (EM1)

Factors and Multiples

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Study Notes & Exam Tips

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Study Notes

Factors and multiples are fundamental concepts in mathematics that help in understanding numbers and their relationships.

Multiples — numbers that a given number can divide into without leaving a remainder. Example: The multiples of 3 are 3, 6, 9, 12, 15...
Common Multiples — numbers that are multiples of two or more numbers. Example: 40 is a common multiple of 4 and 5.
Lowest Common Multiple (LCM) — the smallest number that is a multiple of two or more numbers. Example: The LCM of 4 and 5 is 20.
Factors — numbers that divide exactly into another number. Example: The factors of 8 are 1, 2, 4, 8.
Common Factors — numbers that are factors of two or more numbers. Example: 2, 5, and 10 are common factors of 30 and 20.
Highest Common Factor (HCF) — the greatest factor that divides two or more numbers. Example: The HCF of 30 and 36 is 6.

Exam Tips

Key Definitions to Remember

Multiples are numbers that a given number can divide into without a remainder.
Common multiples are numbers that are multiples of two or more numbers.
The lowest common multiple (LCM) is the smallest common multiple of two or more numbers.
Factors are numbers that divide exactly into another number.
Common factors are numbers that are factors of two or more numbers.
The highest common factor (HCF) is the greatest factor that divides two or more numbers.

Common Confusions

Confusing factors with multiples.
Mixing up LCM and HCF.

Typical Exam Questions

What are the multiples of 4? 4, 8, 12, 16, 20...
Find the LCM of 3 and 6? 6
What is the HCF of 30 and 36? 6

What Examiners Usually Test

Ability to list factors and multiples.
Finding common multiples and factors.
Calculating LCM and HCF using different methods.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

AI-marked quiz

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