N1: Numbers and their operations

Write a positive integer as a product of prime powers. The highest common factor takes the smaller shared power of each prime, while the lowest common multiple takes the larger power appearing in either number. The same factor tree can also reveal exact square and cube roots when every prime exponent is divisible by $2$ or $3$.

Integers include negative whole numbers and zero. Rational numbers can be written as a fraction of integers, while irrational numbers cannot. All rational and irrational numbers form the real numbers. On a number line, values increase to the right; multiplying or dividing an inequality by a negative number reverses its direction.

Apply the four operations with sign discipline. Brackets and powers are evaluated before multiplication and division, followed by addition and subtraction. Keep exact fractions or surds until an approximation is requested.

For decimal places, count digits after the decimal point. For significant figures, begin at the first non-zero digit. Estimate by rounding each input to a convenient value, then compare the estimate with the calculator result.

Standard form is $A \times 10^n$, where $1 \leq A < 10$ and $n$ is an integer. Multiplication combines powers of ten; addition requires both terms to use the same power first.

Index laws apply to a common base. A negative index means reciprocal, a zero index gives $1$ for a non-zero base, and a fractional index combines a root with a power. Rewrite unfamiliar expressions with one base before simplifying.