Find the HCF of the following. Use index notation. a 63, 42 and 21 b 144, 216 and 360 c 280, 105 and 175 d 126, 234 and 90 e 160, 96 and 224 f 189, 270 and 108 g 288, 180 and 108

Common prime factors are 3 and 7.
Lowest power of 3: $3^1$
Lowest power of 7: $7^1$

The HCF for part a is $\boxed{21}$.

Common prime factors are 2 and 3.
Lowest power of 2: $2^3$
Lowest power of 3: $3^2$

The HCF for part b is $\boxed{72}$.

Common prime factors are 5 and 7.
Lowest power of 5: $5^1$
Lowest power of 7: $7^1$

The HCF for part c is $\boxed{35}$.

Common prime factors are 2 and 3.
Lowest power of 2: $2^1$
Lowest power of 3: $3^2$

The HCF for part d is $\boxed{18}$.

The only common prime factor is 2.
Lowest power of 2: $2^5$

The HCF for part e is $\boxed{32}$.

The only common prime factor is 3.
Lowest power of 3: $3^3$

The HCF for part f is $\boxed{27}$.

Common prime factors are 2 and 3.
Lowest power of 2: $2^2$
Lowest power of 3: $3^2$

The HCF for part g is $\boxed{36}$.