A number when divided by 108 leaves a remainder of 79. What would be the remainder if the same number is divided by 18?

Steps to Solve

1. Express the given information as an equation

Let the number be $n$. We are given that when $n$ is divided by 108, the remainder is 79. We can write this as: $n = 108q + 79$, where $q$ is the quotient.

2. Rewrite the equation to find the remainder when divided by 18

We want to find the remainder when $n$ is divided by 18. Since $108 = 18 \times 6$, we can rewrite the equation as: $n = (18 \times 6)q + 79$.

3. Isolate the multiples of 18

We can rewrite 79 as a multiple of 18 plus a remainder. Divide 79 by 18: $79 = 18 \times 4 + 7$.

4. Substitute back into the equation and simplify

Now, substitute this back into the equation for $n$: $n = (18 \times 6)q + (18 \times 4 + 7)$ $n = 18(6q) + 18(4) + 7$ $n = 18(6q + 4) + 7$

5. Determine the remainder

From the equation $n = 18(6q + 4) + 7$, we can see that when $n$ is divided by 18, the quotient is $6q + 4$ and the remainder is 7.