# Number Theory

## 5 files30/11/2016

(a) Understand key terms such as perfect square, integer, positive integer, non-negative integers.

(b) Prime factorise a number and use to find the LCM, HCF of two numbers. Understand when numbers are 'coprime'.

(c) Know the divisibility laws from 3 to 11 and be able to break down into multiple divisibility rules for larger numbers. Use these rules to mentally prime factorise numbers rapidly and have a sense if a number is prime. (d) Find factors of a number using its prime factorisation (e.g. is 20 a factor of 2^{4} x 3 x 5^{3}?) and determine the number of factors of a number.

Extension: (i) Reason about divisibility on each side of an equation and of terms, and find integer solutions to linear equations (i.e. linear Diophantine equations).

(ii) Further uses of prime factorisations: (1) Squares and cubes (2) Trailing zeroes.