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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

In this page, a simple overview of the divisibility test for `3` is provided.



click on the content to continue..

Which of the following are multiples of `3`?

  • `3,6,9,12,15,18,21,24,27,30,33, cdots`
  • `3,6,9,12,15,18,21,24,27,30,33, cdots`
  • `10,20,30,40,cdots`

The answer is "`3,6,9,12,15,18,21,24,27,30,33, cdots`"

Consider the numbers `12` and `13`. Which one is divisible by `3`?

Check this by long division method.

  • `13`
  • `12`
  • `12`

The answer is "`12`"

Consider the multiples of `3` given as `3,6,9,12,15,18,21,24,27,30,33, cdots`. Is there any similarity observed in the multiples?

  • all are ending in one of the numbers `3,6,9`
  • sum of all digits is one of the numbers `3, 6, 9`
  • sum of all digits is one of the numbers `3, 6, 9`

The answer is "sum of all digits is one of the numbers `3, 6, 9`".

This is explained as follows
`12 -> 1+2=3` sum is `3`
`15 -> 1+5=6` sum is `6`
`18 -> 1+8=9` sum is `9`
`21 -> 2+1=3` sum is `3`
`24 -> 2+4=6` sum is `6`
`27 -> 2+7=9` sum is `9`

The property is true for all multiples of `3`.

To identify the multiplies of `3`, the sum of all digits of the number is checked for divisibility by `3`.

Explanation for the curious mind.

Consider divisibility test `42` by `3`

To simplify the divisibility test, let us subtract a multiple of the divisor `3`.
Seeing the `10`s place value `4`, we choose the multiple `3xx3xx4 = 36` to subtract from the number.

As per the property of simplification by subtraction, the divisibility test of `42` is simplified into divisibility test of `42-36 = 40-36+2 = 4+2`.

This explains the divisibility test for `3`.

Consider the numbers `12` and `13`. Which one is divisible by `3`?

  • `13`
  • `12`
  • `12`

The answer is "`12`"

Test for Divisibility by 3 : If the sum of all the digits is divisible by `3` then the number is divisible by `3`

Is `318` divisible by `3`?

  • Yes
  • Yes
  • No

The answer is "Yes". Checking the sum of digits `3+1+8=12`. The sum is divisible by `3`. It is concluded that the number is divisible by `3`.

Is `923` divisible by `3`?

  • Yes
  • No
  • No

The answer is "No". Checking sum of the digits `9+2+3 = 14`, it is concluded that the number is NOT divisible by `3`.

                            
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