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What is Divisibility?
When we divide any number (dividend) by any other number(divisor), if the remainder after the division is 0, we say that the dividend was divisible by the divisor.
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 3 or not , because numbers can be as big as in lakhs or crore, and we barely remember multiplication tables.
So it is not possible to remember the 11th or 35th or 67th factor from the multiplication table of 3.
What is Divisibility by 3?
When we divide any number by 3, and the remainder comes out to be 0, we say that the number is divisible by 3 and if the remainder is non 0, we say the number is not divisible by 3.
We can not always actually divide the number by 3 and then check whether the number is divisible or not, so we use the test of divisibility.
The Test of Divisibility of 3:
When the sum of the digits of the number is a multiple of 3, we say that the number is divisible by 3. 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 3, we say that the original number is divisible by 3.
Using this, calculation will be faster,because dividing a larger number by 3 would take a long time.
Example 1 – Checking whether 1053 is divisible by 3 using test of divisibility
Solution: The sum of digits of 1053 is 9, 9 is a multiple of 3, hence number 1053 is divisible by 3.
Example 2- Checking whether 9978 is divisible by 3 using test of divisibility
Solution: The sum of digits of 9978 is 33, 33 is a multiple of 3, hence the number 9978 is divisible by 3.
How does this test of divisibility make your calculations easy?
1. You can use it easily to check LCM(least common multiples) and HCF(highest common factor) :
Example: If you were to find LCM of 3 and 1053, we can clearly see that the sum of digits of 1053 is 9, so 9 is a multiple of 3, hence it is divisible by 3.
LCM will be 1053 itself.
If the number would not have been a factor of 3, we would have used other longer methods of finding LCM and it would have been a greater number.
2. While quick 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 3, we can simply divide both of them by 3 and make our calculations easier.
Example: If we see numbers like 150/33, we simply see common factor 3(as both are divisible by 3), we can simply divide both by 3 and get the simple form- 50/11.
Test of divisibility of 6:
When a number is divisible by 2(having 0,2,4,6 or 8 as the unit place) and also divisible by 3, we say that the number is divisible by 6.
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 102445 is divisible by 3 or not?
Ans.- Given number 102445, the sum of digit= 1+0+2+4+4+5 = 16, 16 is not the multiple of 3, hence the number is not divisible by 3.
Q.2 Simplify: 154 divided by 16 (indirect usage in simplifying)
Ans.- The number 154 and 16 are both not divisible by 3, hence we cannot divide both by the common factor 3, as they are not the multiples of 3
Q.3 Are the given numbers divisible by 3 or not?
33, 5433, 8888
Ans.- The number sum of digits of 33 and the sum of digits of 5433 are both multiples of 3, hence they both are divisible by 3.
But the sum of digits of 8888 is 32, which is not a multiple of 3, so it is not divisible by 3.
Q.4 Find the odd one out?
33,5433,8888
Ans.- The number sum of digits of 33 and the sum of digits of 5433 are both multiples of 3, hence they both are divisible by 3.
But the sum of digits of 8888 is 32, which is not a multiple of 3, so it is not divisible by 3.
Hence , with this logic 8888 is the odd one out.
Conclusion:
Hope this article gave a clear understanding of the concept of divisibility test of 3. This article also makes sure that all the concepts are backed by proper examples so that students might have a better understanding of the topic.
