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Thought-Process to Discover Knowledge

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

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mathsDivisibility in Whole NumbersSimplification of Divisibility Tests: 8, 12, 15

### Divisibility: Simplification by Subtraction

In this page, Simplification of divisibility test by subtraction is explained. This is used to develop other divisibility tests for specific numbers.

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Given a number 83xx2322 = 192726. is it divisible by 83?

• Yes
• Yes
• No
• Can't say

The answer is "Yes". The number is given as a multiple of 83, so it is divisible by 83.

Consider a number 83xx23 + 422 = 2331, Which of the following helps to find if the number is divisible by 83?

• we have to check the large number 2331
• we can check the smaller number 422 which is easier
• we can check the smaller number 422 which is easier

The answer is "we can check the smaller number 422 which is easier".

Consider a number 2331, Which of the following helps to find if it is divisible by 83?

• we have to check the large number 2331
• it can be simplified to a smaller number 2331-83xx20=671 which is easier
• it can be simplified to a smaller number 2331-83xx20=671 which is easier

The answer is "It can be simplified to a smaller number".

To check the divisibility, the following properties are helpful.

•  multiple of a number is divisible by the number.
eg: 3xx423 is a multiple of 3 and so it is divisible by 3.

•  In a sum of two numbers, if one number is a multiple of the divisor, then only the other number is checked for divisibility.
eg: Divisibility test of 3xx423 + 7 by 3, can be simplified to divisibility test of 7, as 3xx423 is a multiple of 3.

•  To check divisibility of a large number by a divisor, it can be simplified into a smaller number by subtracting a multiple of the divisor.
eg: Divisibility test of 913 by 3, can be simplified to divisibility test of 913-300xx3 = 13

The method is named Simplification by Subtraction method.

Simplification by Subtraction for Divisibility Tests: To perform divisibility test on a large number, a multiple of a divisor can be subtracted and the divisibility test is performed on the difference.

Find the divisibility of 777012 by 111.

• Not Divisible. Subtract 777012 - 111xx7000 = 12. Check the divisibility on 12
• Not Divisible. Subtract 777012 - 111xx7000 = 12. Check the divisibility on 12
• It is not simple to check divisibility large numbers

Find the divisibility of 804 by 67.
• Not Divisible. Subtract 804 - 67xx10 = 134. Check the divisibility on 134
• Divisible. 134=67xx2 is divisible by 67
• Divisible. 134=67xx2 is divisible by 67