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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