Question

Question #fc640

Answer 1

See the solution process below:

Explanation:

The factors of each of the numbers are:

`45 = color(red)(3) xx 3 xx 5`

`9 = color(red)(3) xx 3`

`21 = color(red)(3) xx 7`

Therefore the Greatest Common Factor of these three numbers is: `color(red)(3)`

Answer 2

The Greatest/Highest common factor (GCF or HCF) of 45, 9 and 21 is 3...

Explanation:

Unlike the other answers, this method will be helpful when determining the HCF or GCF of not only larger numbers, but also bigger sets of numbers. This method is full proof and will require basic knowledge of prime decomposition and exponential laws.

Firstly, we individually prime decompose the set of numbers:

= `45` = `3^2 * 5`
= `9` = `3^2`
= `21` = `3*7`

We then will have to find the product of the common exponents. For example, the only common number is `3^1`. Note that the procedure for finding the GCF is virtually the opposite to that of finding the LCM of a set of numbers:

= `3^1`
= `3`

Therefore, the GCF of 45, 9 and 21 is 3.

All the best!

Answer 3

3

Explanation:

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