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The prime factorization of 120 is
.
Solución
To find the prime factorization of 120, we’ll break it down into its prime components step by step.
Step 1: Divide by the Smallest Prime Number (2)
120 is even, so we start by dividing by 2.
Step 2: Continue Dividing by 2
60 is also even.
Now, 2 is no longer a factor of 15.
Step 3: Move to the Next Prime Number (3)
15 is divisible by 3.
Step 4: Finally, Divide by the Last Prime Number (5)
5 is a prime number.
Putting It All Together
The prime factors we used are:
This can be expressed using exponents as:
Prime Factorization of 120
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Beyond the Answer
To find the prime factorization of 120, you start by dividing 120 by the smallest prime number, which is 2. Doing this, you get 120 ÷ 2 = 60. Dividing 60 by 2 again gives you 30, and dividing 30 by 2 one more time results in 15. Since 15 isn’t divisible by 2, you move on to the next prime number, which is 3. Dividing 15 by 3 gives you 5, and since 5 is a prime number, you can stop here. Thus, the prime factorization of 120 is 2³ × 3¹ × 5¹.
Now, if you want to see this factorization in action, think about how it’s integral to everyday life! For example, if you’re slicing a pizza into 120 equal pieces for a party, knowing the prime factorization allows you to easily alter the number of slices if you need to serve a different number of guests. This magical math helps in optimizing portions and ensuring everyone gets their fair share of cheesy goodness!

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