Question

The number 3 13 -3 10 is divisible by

Answer 1

Answer:

3^13-3^10

=3^10(3^3-1)

=3^10*26

=3^10*2*13

So it will be divisible by 2,3,13

Answer 2

Answer:

Step-by-step explanation:

Concept:

The concept of tests of divisibility will be used to get the solution of this question.

Given:

The number which is given is  $3^{13} -3^{10}$ .

To find:

We have to find the numbers  which will divide $3^{13} -3^{10}$ .

Solution:

When solving problems of this type of questions, it is sufficient to simplify the expression. There is no need to keep figuring out the values of $3^{13}$ and $3^{10}$ . There is a potential that mistakes will be made and it will take a long time.

To make it simpler, let's use $3^{10}$ as the common value.

then determine the value of $(3^{3} -1)$, and by determining whether the resulting expression is divisible, we may get the solution.

Then $3^{13} -3^{10}=3^{10}(3^{3}-1)$

The value of $3^{3}$ is $27$ .

So we can write the expression as $3^{10}(27-1)=3^{10} \times 26$ .

As can be seen, it is a multiple of both $2$ and $13$.

As a result, it is also divisible by  $2$ and $13$.

So the number  $3^{13} -3^{10}$ is divisible by $2,3$ and $13$ .

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