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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 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 10s 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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