2.2 Prime factorisation, HCF and LCM — Practise with help

1. Yes; 1 and 13.
2. For example, 1 and 6.

Divide by 2 while the result is even.

$48=2\times24=2\times2\times12=2\times2\times2\times6$.

$48=2\times2\times2\times2\times3=2^4\times3$.

Write each number as prime factors and take shared primes with smaller powers.

$18=2\times3^2$ and $30=2\times3\times5$.

The shared factors are $2\times3=6$, so the HCF is 6.

Use each prime with its greater power.

$8=2^3$ and $12=2^2\times3$.

$2^3\times3=24$, so the LCM is 24.