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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 `8` is provided. The procedure uses simplification by subtraction.



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Consider `1000` and `224`. Which of these is divisible by `8`?

Check this by long division method.

  • `1000`
  • `224`
  • both the above
  • both the above

The answer is "both `1000` and `224`"

The multiples of `8` have the property that lowest `3` digits (hundreds, tens and units) is divisible by `8`.

Explanation for the curious mind
A large number `2344` can be given in the form `2xx1000+344`.
It is learned that if one addend is divisible, then the divisibility test can be performed only on the second addend.
`2xx1000` is divisible by `8` as `1000=125xx8`.
So the divisibility test is performed on `344`, that is the last `3` digits of the number.

Test for Divisibility by `8` : If the last three digits of the dividend is divisible by `8`, then the dividend is divisible by `8`.

Is `2018` divisible by `8`?

  • Yes
  • No
  • No

The answer is "No". Checking the last three digits `18`. As `18` is not a multiple of `8`, it is concluded that the number is not divisible by `8`.

Is `7120` divisible by `8`?

  • Yes
  • Yes
  • No

The answer is "Yes". Checking the last three digits `120`. As `120` is a multiple of `8`, it is concluded that the number is divisible by `8`.

Is `73524` divisible by `8`?

  • Yes
  • No
  • No

The answer is "No". Checking the last three digits `524`. The divisibility test can be simplified by subtraction (`524-400-80-40`) or simplified by factors (`(524,8)` simplified to `(262,4)`, then to `(131,2)`).

                            
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