Question

Which of the following numbers is divisible by \[13\]?
A). \[1573\]
B). \[2983\]
C). \[2971\]
D). $2974$

Answer 1

Hint: We need to find which number from the options is divisible by [13\]. We have to use the divisibility test of \[13\] to find the number which is divisible by \[13\].
Divisibility test of \[13\]: To check whether the given number is divisible by \[13\] or not, multiply the last digit by $4$and add this number to the number formed by remaining digits(except last digit). Now if this addition is divisible by \[13\], then the number is divisible by \[13\], else the given number is not divisible by \[13\].

Complete step-by-step solution:
We have to find which number from the options is divisible by \[13\]. We will use a divisibility test of $13$ to find the number which is divisible by \[13\].
Let us check all the options to find the number which is divisible by \[13\],
Let us check if $1573$ is divisible by $13$ or not,
Let us apply the divisibility test of $13$.
Let us multiply the last digit of $1573$ by $4$,
$3 \times 4 = 12$
Let us add this number to the number formed by remaining digits(except last digit).
$157 + 12 = 169$
Let us check if this addition is divisible by \[13\],
$169$ is divisible by $13$, hence $1573$ is divisible by $13$.
Hence option A) $1573$ is correct.
Let us check if $2983$ is divisible by $13$ or not,
Let us apply the divisibility test of $13$.
Let us multiply the last digit of $2983$ by $4$,
$3 \times 4 = 12$
Let us add this number to the number formed by remaining digits(except last digit).
$298 + 12 = 310$
Let us check if this addition is divisible by \[13\],
$310$is not divisible by $13$, hence $2983$ is not divisible by $13$.
Hence option B) $2983$ is incorrect.
Let us check if $2971$ is divisible by $13$ or not,
Let us apply the divisibility test of $13$.
Let us multiply the last digit of $2971$by$4$,
$1 \times 4 = 4$
Let us add this number to the number formed by remaining digits(except last digit).
$297 + 4 = 301$
Let us check if this addition is divisible by \[13\],
$301$is not divisible by $13$, hence $2971$ is not divisible by $13$.
Hence option C) $2971$ is incorrect.
Let us check if $2974$ is divisible by $13$ or not,
Let us apply the divisibility test of $13$.
Let us multiply the last digit of $2974$ by $4$,
$4 \times 4 = 16$
Let us add this number to the number formed by remaining digits(except last digit).
$297 + 16 = 313$
Let us check if this addition is divisible by \[13\],
$313$ is not divisible by $13$, hence $2974$ is not divisible by $13$.
Hence option C) $2974$ is incorrect.
Hence option A) $1573$ is correct.

Note: The number divisible by $13$can also be found by performing actual division and checking if the number is perfectly divisible or not . But that is a lengthy and time consuming process, so it's better to use the divisibility test, which will minimize calculations and will give answers in a shorter time.