Mathematics
High School (9–10)
General
Number Systems › Divisibility, HCF and LCMNumber Systems › Rational and Irrational NumbersChapter 2Real Numbers
Every whole number above 1 is built from primes in exactly one way. This one fact finds the HCF and the LCM of any numbers, and it proves that a number such as the square root of 2 can never be written as a fraction. In this chapter you break numbers into primes, solve problems about bells, tiles and buses with the HCF and the LCM, and learn how to prove that a number is irrational. Python checks your work and finds patterns in thousands of numbers.
Part of Mathematics · High School (9–10) (chapter 2)
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Primes, HCF and LCM
Break any number into primes, and see why there is only one way to do it. Then use the primes to find the HCF and the LCM, and solve real problems with them: bells that ring together, the largest tile for a floor, and buses that meet again.
Irrational Numbers and Proofs
Why can the square root of 2 never be a fraction? Learn to prove it, step by step, with a proof by contradiction. Then prove the same for other roots, and find out when a sum or a product of such numbers is irrational.