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The step diagram method of prime factorization involves dividing the given number by the smallest prime possible, then repeating with the resulting quotient. The smallest prime that even divides into 75 is 3, so we note
3 and divide through:
. The smallest prime that evenly divides 25 is 5, so we note
5 and divide through:
. 5 itsself is prime so we note 5 again and arrive at:
. Since we arrive at one, this means we have completed the factorization. Therefore, the prime factorization of 75 is 3*5*5, or
.
We can check to make sure by multiplying the three and making sure their product is 75. 3*5 = 15 and 15*5 =75, so that works out.
The standard notation for this method is hard for me to display here, so I have provided a link that shows how it is typically formatted on the first page (right column): http://go.hrw.com/resources/go_mt/hm2/so/c2ch2bso.pdf
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