Factors and Multiples
Understanding the concepts of factors and multiples of a number.
Core concept
Every number is both a factor and a multiple of itself, and 1 is a factor of every number. While every number has a finite, limited set of factors, every number has an infinite number of multiples. Understanding factors and multiples is essential for simplifying fractions, finding common denominators, and solving problems involving equal grouping or sharing.
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Key diagram

- Show a factor tree for 12 and a list of the first five multiples of 4.
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Quick notes
• A factor divides a number exactly, with no remainder.
• A multiple is obtained by multiplying a number by a whole number.
• Every number has a limited (finite) set of factors but infinite multiples.
• 1 is a factor of every number; every number is a factor and multiple of itself.