# Thread: prime factorization: using a factor tree to factor 400

1. ## prime factorization: using a factor tree to factor 400

HI do not get how to properly how to draw a factor tree , my question is what is the prime factorization of 400?

2. I do not know much about tree diagrams.

But $400 = $$2^4$$$$5^2$$$.

3. When you are trying to factor a number in general, the best thing to do is to try to divide it by 2, the smallest prime. Since your number, 400, is even, 2 will divide into it. Start the "tree" by drawing "branches" hanging down from the "top":

Code:
   400
/   \
200    2
Since "2" is prime, you can't factor the "2" branch, so you leave that alone. Turning to the "200" branch, you see that it is even, so you can divide by 2 again, leaving 100, which is also even, so:

Code:
    400
/   \
200   2
/ \
100  2
Then continue on in the same manner, until each "branch" ends with a prime number. Here's what yours looks like:

Code:
        400
/  \
200   2
/  \
100   2
/  \
50   2
/\
10  5
/\
5  2
The factored form (the answer they're looking for) is all the prime numbers at the ends of the "branches". In this case, that's 5, 2, 5, 2, 2, 2. To put the answer in the correct form, group the factors: 2, 2, 2, 2, 5, 5. Then write the list in product form, using powers: (2^4)(5^2).

Note: The carate symbol (the "^" sign) indicates exponents, so "5^2" means "five squared".
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Edited by stapel -- Reason for edit: punctuation, spelling, mathematical accuracy, spacing, etc

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