prime factorization of 484
Understand the Problem
The question is asking for the prime factorization of the number 484, which involves breaking it down into its prime number components.
Answer
The prime factorization of 484 is $2^2 \cdot 11^2$.
Answer for screen readers
The prime factorization of 484 is $2^2 \cdot 11^2$.
Steps to Solve
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Identify the number to factor We start with the number 484.
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Check for divisibility by the smallest prime The smallest prime number is 2. We check if 484 is even (which it is) and divide by 2: $$ 484 \div 2 = 242 $$
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Repeat the division by 2 Next, we take the result 242 and check again for divisibility by 2: $$ 242 \div 2 = 121 $$
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Check divisibility by the next primes Now we have 121. This number is odd, so we check for divisibility by the next smallest prime, which is 3 (it is not divisible), then 5 (not divisible), and finally we check 11: $$ 121 \div 11 = 11 $$
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Final division of the prime number Now we repeat for 11, since $11 \div 11 = 1$. We end with the factorizations: $$ 484 = 2^2 \cdot 11^2 $$
The prime factorization of 484 is $2^2 \cdot 11^2$.
More Information
The number 484 is notable because it is a perfect square, specifically $22^2$, which also correlates with its prime factorization being squared components.
Tips
- Mistaking 121 for being prime when it is actually $11^2$.
- Forgetting to check divisibility by further primes once you reach an odd number.
