Find the HCF of the following. Leave the answers as prime factors. a 2×3×3×5; 2×2×3×3×3; 3×3×5×7

The common prime factor is 3.

3 appears twice in $N_1$ ($3^2$), three times in $N_2$ ($3^3$), and twice in $N_3$ ($3^2$). The lowest power is $3^2$.

The HCF for a) is $\boxed{3 \times 3}$

The common prime factors are 2 and 3.

For 2: $2^2$ in $N_1$, $2^2$ in $N_2$, $2^1$ in $N_3$. The lowest power is $2^1$.
For 3: $3^1$ in $N_1$, $3^2$ in $N_2$, $3^2$ in $N_3$. The lowest power is $3^1$.

The HCF for b) is $\boxed{2 \times 3}$

The common prime factors are 2 and 5.

For 2: $2^1$ in $N_1$, $2^3$ in $N_2$, $2^2$ in $N_3$. The lowest power is $2^1$.
For 5: $5^1$ in $N_1$, $5^1$ in $N_2$, $5^1$ in $N_3$. The lowest power is $5^1$.

The HCF for c) is $\boxed{2 \times 5}$

The common prime factors are 2 and 3.

For 2: $2^3$ in $N_1$, $2^2$ in $N_2$, $2^1$ in $N_3$. The lowest power is $2^1$.
For 3: $3^2$ in $N_1$, $3^3$ in $N_2$, $3^3$ in $N_3$. The lowest power is $3^2$.

The HCF for d) is $\boxed{2 \times 3 \times 3}$

The common prime factors are 3, 5, and 7.

For 3: $3^2$ in $N_1$, $3^1$ in $N_2$, $3^1$ in $N_3$. The lowest power is $3^1$.
For 5: $5^1$ in $N_1$, $5^2$ in $N_2$, $5^2$ in $N_3$. The lowest power is $5^1$.
For 7: $7^1$ in $N_1$, $7^2$ in $N_2$, $7^1$ in $N_3$. The lowest power is $7^1$.

The HCF for e) is $\boxed{3 \times 5 \times 7}$