What is the prime factorization of 176?
Understand the Problem
The question is asking for the prime factorization of the number 176, which means we need to express 176 as a product of its prime factors.
Answer
The prime factorization of 176 is $2^4 \times 11$.
Answer for screen readers
The prime factorization of 176 is $2^4 \times 11$.
Steps to Solve
- Divide by the smallest prime number Start by dividing 176 by the smallest prime number, which is 2.
$$ 176 \div 2 = 88 $$
- Continue dividing by 2 Now take 88 and divide it by 2 again, since it is also even.
$$ 88 \div 2 = 44 $$
- Keep dividing by 2 Next, divide 44 by 2 once more.
$$ 44 \div 2 = 22 $$
- Final division by 2 Now, divide 22 by 2.
$$ 22 \div 2 = 11 $$
- Identify the prime factors At this point, we can no longer divide by 2 because 11 is a prime number.
So, the prime factorization of 176 is:
$$ 176 = 2^4 \times 11 $$
The prime factorization of 176 is $2^4 \times 11$.
More Information
The prime factorization tells us that 176 can be expressed as the product of the prime number 2, raised to the 4th power, and the prime number 11. This method is useful in number theory and can help simplify fractions or find the greatest common divisor (GCD) of numbers.
Tips
- A common mistake is forgetting to continue dividing until reaching a prime number, resulting in an incomplete factorization. Always check if the resulting number can still be divided by a prime.
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