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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.
mathsDivisibility in Whole NumbersHighest Common Factor

### HCF Division Method

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

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Consider two numbers with HCF n. The numbers can be given in the form nxxp and nxxq.

For example, HCF 36 and 48 is 12. And 36=12xx3 and 48=12xx4. In this example n=12, p=3 and q=4.

The p and q are derived from non-common prime factors of the two numbers.

Let us consider that nxxq is the larger than nxxp.

To simplify finding HCF, the larger number is subtracted by a multiple of the smaller number. That is, nxxq - mxxnxxp is the difference, where m is randomly chosen.

What is the HCF of the two numbers nxxp and nxxq-mxxnxxq?

• same as the HCF of nxxp and nxxq
• the HCF cannot be found with modified numbers
• the HCF cannot be found with modified numbers

The answer is "same as the HCF of nxxp and nxxq".

It was learned that HCF of two numbers nxxp and nxxq is same as the HCF of nxxp and nxxq - mxxnxxp for any m. Using this property, a simplified procedure is devised. The simplified procedure is given in the figure.

•  The numbers are placed in long division form

•  A multiple of smaller number is subtracted from the larger number (420-280).

•  Now, the difference and the smaller number are the pair for which the HCF is to be found. repeat the procedure in the next step. The step in which the difference is 0, the smaller number in that step is the HCF.

Division Method to find HCF : To find HCF of two large numbers :

•  The numbers are placed in long division form

•  A multiple of smaller number is subtracted from the larger number.

•  Now, the difference and the smaller number are the pair for which the HCF is to be found. repeat the procedure in the next step. The step in which the difference is 0, the smaller number in that step is the HCF. An example is illustrated in the figure.

Find HCF of 336 and 72.

• 24
• 24
• 12

The answer is "24".

slide-show version coming soon