Divisibility Test of 15

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 is a simple concept which is quick, easy to remember and a helpful trick to solve  all your math questions with accuracy and speed.

We cannot always use the multiplication table to check whether any number is a factor of 15 or not , because numbers can be as big as in lakhs or crore, and we barely remember multiplication tables. But with a simple trick, we can check the divisibility in seconds.

So it is not possible to remember the 11th or 35th or 67th factor from the multiplication table of 15.

What is the test of divisibility by 15?

A number is said to be divisible by 15, when on dividing it leaves the remainder 0, if it does not leave the remainder 0, then it is said to be non divisible by 15.

So to give prompt answers, we need a test of divisibility, because everytime we cannot use long division to find whether a number is divisible or not.

When do we say that the number is divisible by 15 or the test of divisibility is passed?

A number when divided by 15, is said to be divisible by 15, when it is divisible by both 5 and 3. When both the test of divisibility 5 and 3 are passed, we can affirm that the given number is divisible by 15.

• Divisibility By 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.

We take help from the multiplication table to remember, when we see the sum of digits like 21,18 or 33, etc and check whether the sum is a multiple of 3 or not.

• Divisibility By 5:

When the unit place digit of a number is either 5, or 0, we say that the number is divisible by 5 and passed the test of divisibility.

Special case of 0: even though some may argue that the number 0 also have 0 at unit’s place, then why can’t it be considered divisible by 5, as per what mathematician had said-

0 divided by any number is not defined in math.

NOTE: For being divisible by 15, both conditions of the test of divisibility of 3 and 5 must be satisfied.

Using this, calculation will be faster,because dividing a larger number by 15 would take a long time:

Example 1 –  Checking whether 1035 is divisible by 15 using test of divisibility

And.- The sum of digits of 1035 is 9, 9 is a multiple of 3, hence number 1053 is divisible by 3. Now the unit place digit of 1035 is 5, hence the number is divisible by 5. Therefore both the conditions are satisfied , hence the number is divisible by 15.

Example 2-  Checking whether 9978 is divisible by 15 using test of divisibility

The sum of digits of 9978 is 33, 33 is a multiple of 3, hence the  number 9978 is divisible by 3. But the unit digit of the number is neither 0 nor 5, so it is not divisible by 5. Hence both conditions are not satisfied, therefore the number is not divisible by 15.

Example 3-  Checking whether 325 is divisible by 15 using test of divisibility

The unit place of 325 has 5, therefore, it is divisible by 5, but the sum of digits is not a multiple of 3, hence both conditions are not satisfied,therefore the number is not divisible by 15.

How does this test of divisibility make your calculations easy?

1. Do 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 15, we can simply divide both of them by 15 and make our calculations easier.

Example:  If we see numbers like 150/45, we simply see common factor 15(as both are divisible by 15), we can simply divide both by 15 and get the simple form- 10/3.

2. Direct questions of test divisibility asked in various exams, and also helps in solving various logic based or series pattern based questions.

3. Finding the odd in  “odd one out” type of questions

Now few examples of questions on the topic: 

Q.1 Find whether the number 102435 is divisible by 3 or not?

Ans.- given number 102445, the sum of digit= 1+0+2+4+3+5 =  15, 15 is a multiple of 3, hence the number is divisible by 3.

As the unit place of the number is 5, hence it is divisible by 5 too.

Hence both conditions are satisfied and the number is divisible by 15.

Q.2  Simplify: 150 divided by 45(indirect usage in simplifying)

Ans.- 150/45, we simply see common factor 15(as both are divisible by 15), we can simply divide both by 15 and get the simple form- 10/3.

Q.3 Are the given numbers divisible by 15 or not?

 45, 5415

Ans.-  The number 45 and 5415 are both divisible by 3, as the sum of digits is a multiple of 3, and both unit place 5, hence are divisible by 5.

Therefore both conditions are satisfied, and both are divisible by 15.

Q.4 Find the odd one out?

• 45, 5415, 8888

Ans.-. The number 45 and 5415 are both divisible by 3, as the sum of digits is a multiple of 3, and both unit place 5, hence are divisible by 5.

Therefore both conditions are satisfied, and both are divisible by 15.

But the number 8888 is neither divisible 3, nor 5, therefore it is not divisible by 15.

Conclusion

This article has given a clear concept of the divisibility test of 15 through proper explanations and examples. Hope this article has provided the students with all the insights that need in-depth understanding.