Multiples, prime factors and factors

Multiples

A multiple of a number is the product of that number and any whole number. For instance, the multiples of 2 are 2, 4, 6, 8, 10 and so on.
The multiples of a number are always equal to or greater than the original number. For example, the multiples of 5 are all equal to 5 or are greater than 5.

Factors

A factor of a number is a whole number that can be divided exactly into another number. For instance, the factors of 10 are 1, 2, 5, and 10.
Every number has at least two factors, 1 and the number itself.
A number that only has two factors, 1 and itself, is a prime number. All other numbers are called composite numbers.

Prime Factors

Prime factorisation is the process of breaking down a composite number into its prime factors.
Every composite number can be expressed as a product of its prime factors. This is known as the Fundamental Theorem of Arithmetic.
To find the prime factors of a number, divide the number by the smallest prime number (i.e., 2) and continue dividing until you can no longer divide evenly.
For instance, the prime factorisation of 36 is 2 × 2 × 3 × 3 or 2^2 × 3^2 in index notation.

Common Multiples and Factors

A common multiple is a number that is a multiple of two or more numbers. For example, 12 is a common multiple of 2, 3, 4 and 6.
A common factor is a factor that two or more numbers share. For instance, 3 is a common factor of 9 and 15.
The Least Common Multiple (LCM) and the Highest Common Factor (HCF) of two or more numbers are useful in many mathematical calculations.

Real-life Applications

Understanding factors, multiples and primes can help in problem-solving and real-life applications such as planning schedules, organising data, simplifying large numbers, and recognising patterns in numbers.