Question

Is the number $12345$ divisible by $15$ ?

Answer 1

Hint: For answering this question we will use the rules of divisibility and get the required answer. For a number to be divisible by 15, it must be divisible by its factors, i.e both 3 and 5. Now, try to recollect the divisibility rules for both 3 and 5 and then figure out whether the number 12345 is divisible by 15 or not.

Complete step by step answer:
Now considering from the question we have a number $12345$ and we should check whether it is divisible by $15$ or not. The divisibility rule states that for a number to be divisible by $15$ it should be divisible by both $3$ and $5$ says its divisibility rule. The divisibility rule for $5$ says that the number to be divisible by $5$ it should have $0$ or $5$ as one’s digit. For the number to be divisible by $3$ the sum of all digits should be a multiple of $3$ .
For the number $12345$ we have $5$ in one’s digit so it is divisible by $5$ .
The sum of all digits of $12345$ is $1+2+3+4+5=15$ as $15$ is a multiple of $3$ it is divisible by $3$ .
As it is divisible by both $3$ and $5$ it is also divisible by $15$ .

Hence we can conclude that the number $12345$ is divisible by $15$ .

Note: For answering this question we have another way that is by performing the traditional division method between $12345$ and $15$, verify it. Now after performing the traditional division we will have $\dfrac{12345}{15}=\dfrac{4115}{5}=823$ . Hence we can conclude that the number $12345$ is perfectly divisible by $15$ .