# Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF

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1.5Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF

In these revision notes for Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF, we cover the following key points:

• What are multiples of a number?
• What are factors of a number?
• How to find the factors of a number?
• What are prime numbers? What do we call a number that is not prime?
• How to write a number as a product of prime factors?
• Why is the least common multiple of two or more numbers so important?
• Why is the greatest common factor of two or more numbers so important?
• How to calculate the least common multiple and greatest common factor of two or more numbers?
• How are these two concepts (LCM and GCF) applied in practice?

## Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF Revision Notes

In simple words, multiples of a number are those numbers that are in the same row (or column) in the times table.

In more formal terms, multiples of a number N are those numbers, which the number N divides without remainder.

Factors on the other hand, are the inverse of multiples. By definition, a factor is a divisor of a number if the division is done without remainder.

By definition, prime numbers are those numbers that are divisible only by 1 and by themselves. Numbers that are not prime are composite.

The number 1 is neither a prime number (as it is only divisible by 1 [that corresponds to itself]) nor a composite number as it is not divisible with other numbers. It is a kind of special number.

The Tabular method is very suitable for finding the prime factors of big numbers and has other useful applications.

We can find the common multiples of two or more small numbers by writing all multiples for each number and then, highlighting the common multiples. It is sufficient to find the smallest of the multiples (known as Least Common Multiple, or LCM) and then, multiply it by 2, 3, 4, ... etc., to find all common multiples of two or more numbers.

Another very important thing to identify and calculate in a set of two or more numbers is the greatest common factor (GCF). It represents the greatest number by which both original numbers are divided.

Both LCM and GCF can be calculated using the tabular method and have a wide range of applications in practice.

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