Question

Write the prime factorization of each number in e-g. e. 25 f. 100g. 16​

Answer 1

Answers:

25 = 5*5 which is the same as 25 = 5^2

100 = 2*2*5*5 which is the same as 100 = 2^2*5^2

16 = 2*2*2*2 which is the same as 16 = 2^4

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Explanation:

To find the prime factorization of 25, we divide by prime numbers. We see that 25/2 = 12.5 isn't a whole number, and neither is 25/3 = 8.33 (approx). But 25/5 = 5 is a whole number. The result is a prime number so we can stop here. This shows that 25 = 5*5 = 5^2

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We'll do the same for 100 as well. Start with dividing over 2

100/2 = 50

50/2 = 25

we can't do 25/2 as mentioned earlier, but we can say 25/5 = 5

So basically 100 = 2*2*25 = 2*2*5*5 = 2^2*5^2

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The same will happen with 16 as well. We divide by 2 until we arrive at a prime number result

16/2 = 8

8/2 = 4

4/2 = 2

We have three 2's as denominators and that last result 2 is included in the set of prime factors as well to say 16 = 2*2*2*2 = 2^4

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The factor tree for each is shown below. For something like 100, there are a few ways to draw out the tree. The same applies for 16 as well.