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Numerical Properties
infoWhy this? Factors, multiples, primes, powers, and roots reveal the structure of whole numbers and support efficient calculation. HCF and LCM also provide essential tools for simplifying fractions, ratios, and later algebraic work.
scheduleWhy now? Early in Year 7, this unit consolidates number sense and introduces precise terminology that can be applied immediately when simplifying ratios and fractions. It also prepares us for prime factorisation and more advanced index work.
neurologyYou need to know
- A factor of a number is a whole number that divides exactly into that number with no remainder.
- A multiple of a number is the product of that number and an integer, so zero is a multiple of every number.
- Factors divide a number, whereas multiples are produced by multiplying a number.
- A square number is the product of an integer multiplied by itself, for example, 1, 4, 9, 16, 25.
- A cube number is the product of an integer multiplied by itself twice, for example, 1, 8, 27, 64, 125.
- A prime number is a number greater than 1 that has exactly two distinct factors: 1 and itself.
- The square root of a number is a value that, when multiplied by itself, gives the original number.
- The cube root of a number is a value that, when multiplied by itself twice, gives the original number.
- The lowest common multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both.
- The highest common factor (HCF) of two numbers is the largest number that divides both numbers exactly.
rocket_launchYou must be able to
- Determine whether a given number is a factor or a multiple of another number.
- Use and apply the vocabulary of square, cube, and prime numbers accurately in context.
- Calculate the square, square root, cube, and cube root of positive integers, including without a calculator for small numbers.
- List the first five positive multiples of any given positive integer.
- List all the factors of any given positive integer.
- Identify the lowest common multiple (LCM) of any two positive integers.
- Identify the highest common factor (HCF) of any two positive integers.
Revision Quiz
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