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Answer
The prime factorization of 360 is
Solution
To find the prime factorization of 360, we’ll break it down into its prime number components step by step.
Step-by-Step Prime Factorization:
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Divide by 2 (the smallest prime number):
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Divide by 2 again:
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Divide by 2 once more:
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Now, 45 is not divisible by 2. Move to the next prime number, which is 3:
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Divide by 3 again:
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Finally, 5 is a prime number and cannot be divided further by other primes.
Putting It All Together:
So, the prime factors of 360 are:
- 2 multiplied by itself three times (
) - 3 multiplied by itself twice (
) - 5 once (
)
Prime Factorization of 360:
Verification:
To ensure the factorization is correct:
This confirms that the prime factorization of 360 is indeed
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Simplify this solution The Deep Dive
To find the prime factorization of 360, we start by dividing it by the smallest prime number, which is 2. We can continue dividing until we can no longer divide evenly:
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
Now, 45 can’t be divided by 2, so we move to the next prime, which is 3:
45 ÷ 3 = 15
15 ÷ 3 = 5
Now we have 5, a prime number.
180 ÷ 2 = 90
90 ÷ 2 = 45
Now, 45 can’t be divided by 2, so we move to the next prime, which is 3:
45 ÷ 3 = 15
15 ÷ 3 = 5
Now we have 5, a prime number.
So, the prime factorization of 360 is 2³ × 3² × 5¹.
To visualize the prime factorization, you can think of building a tower with blocks. Each type of prime number represents a different color block. For 360, you would stack three blocks of 2 (your sturdy base), two blocks of 3 (for a little flair), and one block of 5 (to top it off). Together, they form the impressive tower of 360, showcasing the beauty of multiplication in the world of primes!
Have you ever encountered prime factorization in real-life scenarios? Imagine trying to divide up slices of pizza among friends—knowing the prime factors helps ensure everyone gets an equal share without leftover slices! Whether you’re a math whiz or just trying to figure out the best way to share snacks, prime factorization can come in handy!
