Question

What is a composite number between 300 and 350, whose prime factors are numbers less than 20? What is the prime factorization of this number?

Answer 1

`325 = 5xx5xx13`

Explanation:

`325/5`=65

`65/5` = 13

13 is prime and can not be furthered factored.

so the factors are `5xx 5xx 13`

325 is a composite number between 300 and 350.
All of the prime factors are less than the number 20.
`5 xx 5 xx 13` is the prime factorization of this number.

Answer 2

`19xx2xx3^2=342`

and `300<342<350`

So the criteria has been met

Explanation:

Excerpt from 'Collins Dictionary of Mathematics'

"an integer 'm' that is the product of 2 or more integers other than `+-1` and `+-m`"

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So we will have a choice of composite numbers that can be selected as long as they are between 300 and 350 and are a product of primes

`color(white)(.)`

The question states that we are not allowed to have any factors that is larger than 20 and they have to be prime numbers.

The prime number less than 20 are:

19; 17; 13; 11; 7; 5; 3; 2

I am choosing to work down from the highest.
,.....................................................................................
Consider `350-:19= 18.42..`
`18xx19=342`

So let my chosen number be `342`
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This is a prime factor tree:

`19xx2xx3^2=342`

and `300<342<350`

So the criteria has been met