prime factorization of 612
Understand the Problem
The question is asking for the prime factorization of the number 612, which involves breaking down the number into its prime factors.
Answer
The prime factorization of 612 is $2^2 \times 3^2 \times 17$.
Answer for screen readers
The prime factorization of 612 is $2^2 \times 3^2 \times 17$.
Steps to Solve
-
Start with the number
Begin with the number 612. -
Divide by the smallest prime number
The smallest prime number is 2. Since 612 is even, we can divide it by 2.
$$ 612 \div 2 = 306 $$ -
Repeat with the quotient
Now we have 306. Since it's also even, we divide it by 2 again.
$$ 306 \div 2 = 153 $$ -
Check for divisibility by the next prime numbers
Next, we look at 153. It is not even, so we try the next smallest prime, which is 3.
$$ 153 \div 3 = 51 $$ -
Continue factoring
Next, we factor 51 by 3 again, since $5 + 1 + 3 = 9$, which is divisible by 3.
$$ 51 \div 3 = 17 $$ -
Final prime number
Now we are at 17, which is a prime number, so we stop here. -
Combine results
Now, we have found the prime factors:
$$ 612 = 2^2 \times 3^2 \times 17 $$
The prime factorization of 612 is $2^2 \times 3^2 \times 17$.
More Information
Understanding prime factorization allows us to break down numbers into their fundamental building blocks. This can be useful in various math applications, such as finding the greatest common divisor or simplifying fractions.
Tips
- One common mistake is forgetting to check if the numbers are prime after dividing. Always ensure that you're only left with prime factors at the end.
- Another mistake is dividing by non-prime numbers (like 4, 6, etc.), which can lead you off track.
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