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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 Factorization Method

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. 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. 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.

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