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What is divisibility?
When we divide any number(dividend) by any other number(divisor), whatever the quotient may come, if the remainder is 0, we say that the dividend was divisible by the divisor.
What is divisibility by 18?
Any number divisible by 18, will leave the remainder 0, any non divisible number will not give remainder 0, but we can not always actually divide the number by 18 and then check whether the number is divisible or not, so we use the test of divisibility.
What is the test of divisibility? Why can’t we use a multiplication table?
Tests of divisibility are simple rules, which are easy to remember, and help us quickly solve complex calculations and score marks. We cannot always use the multiplication table to check whether any number is a factor of 18 or not , because numbers can be as big as in lakhs or crore, and we barely remember multiplication tables.
The test of divisibility for 18:
A number when divided by 18, is said to be divisible by 18, when it is divisible by both 2 and 9. When both the test of divisibility 2 and 9 are passed, we say that the given number is divisible by 18.
Divisibility By 9:
When the sum of the digits of the number is a multiple of 9, we say that the number is divisible by 9.
Even if the sum of digits of the number is a large number, we check whether the sum of the digit of this large number is divisible by 9, we affirm that the original number is divisible by 9.
We take help from the multiplication table to remember, when we see the sum of digits like 27,18 or 36, etc and check whether the sum is a multiple of 9 or not.
Divisibility By 2:
If the unit’s digit of the number is 0,2,4,6,or 8, we conclude that the number is divisible by 2.
NOTE: For being divisible by 18, both conditions of the test of divisibility of 2 and 9 must be satisfied.
Using this, calculation will be faster,because dividing a larger number by 18 would take a long time:
Example 1 – checking whether 1080 is divisible by 18 using test of divisibility
The sum of digits of 1080 is 9, 9 is a multiple of 9, hence number 1080 is divisible by 9.
Now the unit place digit of 1080 is 0, hence the number is divisible by 2.
Therefore both the conditions are satisfied , hence the number is divisible by 18.
Example 2- checking whether 5778 is divisible by 18 using test of divisibility
The sum of digits of 5778 is 27, 27 is a multiple of 9, hence the number 5778 is divisible by 9. But the unit digit of the number is 8, so it is divisible by 2.
Hence both conditions are satisfied, therefore the number is divisible by 18.
Example 3- checking whether 322 is divisible by 18 using test of divisibility
The unit place of 322 has 2, therefore, it is divisible by 2, but the sum of digits is not a multiple of 9, hence both conditions are not satisfied, therefore the number is not divisible by 18.
How does this test of divisibility make your calculations easy?
For quick and easy calculations like cancellation, dividing or cross multiplication :
When you are solving mathematics, it’s easier for students to cancel out the common factors quickly, so that the numbers come in their simplest forms, ratios and fractions.
So when we see, if both numbers are divisible by 18, we can simply divide both of them by 15 and make our calculations easier.
Example- If we see numbers like 180/90, we simply see common factor 18(as both are divisible by 18), we can simply divide both by 18 and get the simple form 2/1.
Direct questions of test divisibility asked in various exams, and also helps in solving various logic based or series pattern based questions.
Finding the odd in “odd one out” type of questions
Now few examples of questions on the topic:
Q.1 Find whether the number 146430 is divisible by 18 or not?
Ans.- given number 102445, the sum of digit= 1+4+6+4+3+0 = 18, 18 is a multiple of 9, hence the number is divisible by 9.
As the unit place of the number is 0, hence it is divisible by 2 too.
Hence both conditions are satisfied and the number is divisible by 18.
Q.2 Simplify: 180 divided by 90(indirect usage in simplifying)
Ans.- 180/90, we simply see common factor 18(as both are divisible by 18), we can simply divide both by 18 and get the simple form- 2/1.
Q.3 Are the given numbers divisible by 15 or not?
90,5418
Ans.- The number 90 and 5418 are both divisible by 9, as the sum of digits is a multiple of 9, and both units place 0 or 8, hence are divisible by 2 .
Therefore both conditions are satisfied, and both are divisible by 18.
Q.4 Find the odd one out?
90,5418, 8887
Ans.-. The number 90 and 5418 are both divisible by 9, as the sum of digits is a multiple of 9, and both units place 0 or 8, hence are divisible by 2.
Therefore both conditions are satisfied, and both are divisible by 18.
But the number 8887 is neither divisible by 2 nor be 9,therefore it is not divisible by 18.
Conclusion
This article has given a clear concept of the divisibility test of 18 through proper explanations and examples. Hope this article has provided the students with all the insights that need in-depth understanding.
