Question

Find the remainder when $3 \times 13 \times 23 \times 33 \times \ldots \times 183 \times 193$ is divided by $5$.

Answer 1

209.095.543and 8 tenths

Answer 2

The remainder of the division of
`3 * 13 * 23 * 33 * \ldots * 183 * 193` by 5 is 4

How to determine the remainder of the division

From the question, we have the following parameters that can be used in our computation:

Dividend =
`3 * 13 * 23 * 33 * \ldots * 183 * 193`

Divisor = 5

We can see that

The last digits of the each factor in the dividend is 3

So, we have the last digit of the product to be

Last digit = Last digit of 3²⁰

This is because there are 20 factors in the product

Evaluate

Last digit = 3486784401

The last digit above is 1

So, we have

Remainder = 1/5

Dividing 1 by 5 gives 0 with a remainder of 4

So, we have

Remainder = 4

Hence, the remainder of the division is 4

Question

Find the remainder when
`3 * 13 * 23 * 33 * \ldots * 183 * 193` is divided by 5