Question

Multiply $6341$ by $35$ in the scale of seven.

Answer 1

$6341$ from scale of seven to decimal is $1\times 7^0+4\times 7^1+3\times 7^2+6\times 7^3=2234$

$35$ from scale of seven to decimal is $5\times 7^0+3\times 7^1=26$

Multiplication between them is $=2234\times 26=58084$

Now we need to represent this in scale of $7$ is:

When $58084$ is divided by $7$ quotient is $8297$ and remainder is $5$
When $8297$ is divided by $7$ quotient is $1185$ and remainder is $2$
When $1185$ is divided by $7$ quotient is $169$ and remainder is $2$
When $169$ is divided by $7$ quotient is $24$ and remainder is $1$
When $24$ is divided by $7$ quotient is $3$ and remainder is $3$

When $3$ is divided by $7$ quotient is $0$ and remainder is $3$

Hence, the product is $331225$ in scale of seven.