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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.

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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