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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.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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This page provides a brief overview of finding highest common factor using factorization method.



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Consider finding the HCF of `36` and `48`. Is it simple to list all the factors of the numbers?

  • `36` has `9` factors and `48` has `10` factors. It is not easy to list for larger numbers
  • `36` has `9` factors and `48` has `10` factors. It is not easy to list for larger numbers
  • for any large numbers, listing the factors is simple

The answer is "It becomes hard for large values".

Consider finding the HCF of `36` and `48`. Which of the following helps to simplify the problem?

  • Prime factorization of the numbers
  • Prime factorization of the numbers
  • addition and subtraction of the numbers

The answer is "prime factorization of numbers".

Consider finding the HCF of `36` and `48`.

Prime factorization of `36 = 2xx2xx3xx3`

Prime factorization of `48 = 2xx2xx2xx2xx3`

What part of factor is common between these two?

  • common factors cannot be found
  • `2xx2xx3`
  • `2xx2xx3`

The answer is "`2xx2xx3`".

Consider finding the HCF of `36` and `48`. simplified procedure to find highest common factor A simplified procedure is given in the figure. The numbers are divided successively by common factors. The common factors are multiplied to get HCF.

Factorization Method to find HCF : The numbers are successively divided by common factors. Product of common factors is the HCF.Factorization Method to find highest common factor An example with numbers `36` and `48` are given in the figure.

Find the HCF of `280` and `420`?

Use the Factorization Method to find the HCF.

  • `140`
  • `140`
  • `14`

The answer is "`140`".
The product of common factors is `5xx2xx2xx7`. hcf using factorization method

                            
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