Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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 11 is provided.

click on the content to continue..

Which of the following are multiples of 11?

• 11,22,33, cdots, 110,121,132, cdots
• 10,20,30,40,cdots
• 10,20,30,40,cdots

The answer is "11,22,33, cdots, 110,121,132, cdots"

Consider the multiples of 11 given as 11,22,33, cdots, 110,121,132, cdots. Is there any similarity observed in the multiples? Note: A number 3521 when multiplied by 11 is given as

3521 xx 11
=3521 xx(10+1)
=35210+ 3521
=(3)(5+3)(2+5)(1+2)(1)

Four digit number, when multiplied by 11, results in
• units digit of product is same as that of multiplicand
• tens digit of product is sum of units and tens digit of multiplicand
• hundreds digit of product is sum of tens and hundreds digit of multiplicand
• and so on.

• alternate digits have some pattern
• there is no similarity observed
• there is no similarity observed

The answer is "alternate digits have some pattern".

Consider 121 and 125. Which of these is divisible by 11?

Check this by long division method.

• 121
• 121
• 125
• both the above

The answer is "121".

The multiples of 11 have the property explained below. For example, consider 121 (a multiple of 11).

Add the digits in odd positions 1+1, the result is 2
Add the digits in even positions 2.
Find the difference between these two results.
If the difference is 0 or a multiple of 11, then the number is a divisible by 11.

Test for Divisibility by 11 : Find the sum of digits in even positions and the sum of digits in odd positions. If the difference between these two sums is a multiple of 11, then the number is divisible by 11.

Is 2108 divisible by 11?

• Yes
• No
• No

The answer is "No". The sum of alternate digits are 2+0=2 and 1+8=9. The difference between these sums are 9-2 = 7. Since 7 is not divisible by 11, the number is not divisible by 11.

Is 902 divisible by 11?

• Yes
• Yes
• No

The answer is "Yes". The 9+2-0 = 11, so the number is divisible by 11.

slide-show version coming soon