Question

Find the correct divisibility of 345
\[\begin{align}
  & A.5 \\
 & B.4 \\
 & C.2 \\
 & D.3 \\
\end{align}\]

Answer 1

Hint: For finding the divisibility of 345 by 2, 3, 4, 5 one should use their rules for divisibility. For 2 the number should end with either of the following digits 2, 4, 6, 8, 0. For that of 3, the sum of the digits should be divisible by 3. For that of 4, the numbers last two-digit should be divisible by 4. For 5, the number should end with 5 or 0.

Complete step-by-step solution:
In the question, we have to choose those options which completely divide the number 345.
Before telling that which one divides the number 345, we will first state the divisibility rule of 2, 3, 4, 5, and then test each of them.
So, for the divisibility rule of 2 if the number is even or a number whose last digit is an even number that is 2, 4, 6, 8 including 0 it is always divisible by 2.
For example, let's say 508, its last digit is 8 which is even and divisible by 2. So, it is divisible by 2.
Thus for 345, its last digit is 5 so, as it is odd thus it is not divisible by 2.
For the divisibility rule of 3 if the sum of digit of the number is divisible by 3 then the number itself will be divisible by 3.
For example, let's say 123, its sum of digit is $\left( \text{1}+\text{2}+\text{3} \right)\Rightarrow \text{6}$, which is divisible by 3, hence the number 123 is divisible by 3.
Thus, for 345 its sum of digit is $\left( \text{3}+\text{4}+\text{5} \right)\Rightarrow \text{12}$, which is divisible by 3. Thus, 345 is divisible by 3.
For the divisibility rule of 4, check for the last two digits of the number. If they are divisible by 4 then the number is divisible by 4.
For example, let’s say 108 its last 2 digits is 08, which is divisible by 4 thus the number is divisible by 4.
Thus, for 345 its last 2 digits are 45 which is not divisible by 4. Thus, the number is not divisible by 4.
For the divisibility rule of 5, the last number should be either 0 or 5 then it will be divisible by 5.
For example, let's say 125, its last digit is 5. Thus, it is divisible by 5.
Thus, for 345 its last digit is 5, hence it will be divisible by 5.
So, the correct options are A and D.

Note: Students can also do this problem without knowing the divisibility rule. At first, take every number in the option and try to divide 345 by it. The ones which will divide it without giving remainder are the correct options to the question. So, if we take option A, 5 and then divide 345 by 5, we will get the answer as 69. For option B, if we divide 345 by 4, we will get the quotient as 86 and the remainder as 1. So, it is clear that 345 is divisible by 5 and not by 4. Similarly, we can find options C and D too.