Question

What is the test of divisibility of 18?

Answer 1

Hint: We use the concept of divisibility tests or divisibility rules to check if the given number is divisible by a specified number without using the division method. We are required to determine the divisibility test for the number 18. This can be done by combining the divisibility tests for 2 and 9 since these two numbers are the factors of 18.

Complete step by step solution:
In order to solve this question, let us split the given number as a product of its factors. We know that 18 can be taken as a product of 2 and 9.
$\Rightarrow 18=2\times 9$
Now, to state the test of divisibility for 18, we need to state the test of divisibility for 2 and 9 and combine them.
The divisibility test for 2 is that the last digit in the units place for any given number should be an even number which is a multiple of 2.
The divisibility test for 9 is that the sum of all the digits for the given number should be a multiple of 9. This shows that the given number is divisible by 9.
Therefore, the divisibility test for 18 says that the given number must pass the divisibility tests for both 2 and 9. In other words the given number should be such that its digit in the units place is an even number and the sum of the digits should be a multiple of 9. Then the given number is divisible by 18.

Note: We need to know the basic tests of divisibility for numbers such as 2, 3, 4, 5, 6, etc. Using these, we can derive the tests of divisibility for higher numbers. We need to be careful while factoring these higher valued numbers so we can obtain the test of divisibility correctly.