Question

Which of the these numbers is a factor of $91$?

$3,7,11,13,97$

Answer 1

Step 1: Checking $3$ as a factor of $91$:

$3$ is a factor of $91$ if $3$ divides $91$ exactly. So, dividing $91$ by $3$:

$3309190---1$
Since, remainder is not $0$. Therefore, $3$ is not a factor of $91$.

Step 2: Checking $7$ as a factor of $91$:

$7$ is a factor of $91$ if $7$ divides $91$ exactly. So, dividing $91$ by $7$:

$7139191---0$
Since, remainder is $0$. Therefore, $7$ is a factor of $91$.

Step 3: Checking $11$ as a factor of $91$:

$11$ is a factor of $91$ if $11$ divides $91$ exactly. So, dividing $91$ by $11$:

$1189188---3$
Since, remainder is not $0$. Therefore, $11$ is not a factor of $91$.

Step 4: Checking $13$ as a factor of $91$:

$13$ is a factor of $91$ if $13$ divides $91$ exactly. So, dividing $91$ by $13$:

$1379191---0$
Since, remainder is $0$. Therefore, $13$ is a factor of $91$.

Step 5: Checking $97$ as a factor of $91$:

$97$ is a factor of $91$ if $97$ divides $91$ exactly. So, trying to divide $91$ by $97$:

$9719197----6$
Firstly the above division can't be performed as divisor is greater than dividend.

Secondly the remainder while dividing is always greater or equal to $0$.

Thus, taking note of above facts, we conclude that $97$ is not a factor of $91$.

Hence, from the above $5$ steps, we conclude that only $7$ and $13$ are factors of $91$.