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Learning Outcomes

Classify whole numbers as prime or composite using trial division
Express a composite number as a product of its prime factors using index notation
Find the square root of a perfect square and the cube root of a perfect cube using prime factorisation
Find the smallest value of $k$ that makes a given expression a perfect square or perfect cube
Find the highest common factor (HCF) of two or more numbers using prime factorisation
Find the lowest common multiple (LCM) of two or more numbers using prime factorisation
Apply HCF and LCM to solve real-life problems

Contents▾

Why Primes Matter 1.1Prime Numbers and Composite Numbers 1.2Trial Division 1.3Index Notation and Prime Factorisation 1.4Highest Common Factor (HCF)1.5Lowest Common Multiple (LCM)1.6Real-Life Applications of HCF and LCM 1.7Perfect Squares and Square Roots 1.8Perfect Cubes and Cube Roots 1.9Finding the Smallest k for Perfect Squares and Cubes Chapter Summary

Why Primes Matter

Multiply two large primes together and a computer finishes instantly. Start from the answer and work back to the two primes, and the same computer would still be going long after you had given up. That gap is what keeps your bank details safe online. Scrambling a message that way is encryption, and turning it back is decryption. The two primes are the key. That is why primes are worth knowing properly.

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Questions on Primes, HCF and LCM, marked as you go, with the working shown.

Practise Primes, HCF and LCM

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