prime factor of 484
Understand the Problem
The question is asking for the prime factorization of the number 484, which involves identifying the prime numbers that multiply together to yield the original number.
Answer
The prime factorization of 484 is \( 2^2 \times 11^2 \).
Answer for screen readers
The prime factorization of 484 is ( 2^2 \times 11^2 ).
Steps to Solve
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Divide by Smallest Prime Number
Start by dividing the number 484 by the smallest prime number, which is 2.
$$ 484 \div 2 = 242 $$ -
Continue Dividing by 2
Now take the result, 242, and divide it by 2 again.
$$ 242 \div 2 = 121 $$ -
Switch to Next Prime Number
Now that 121 is not divisible by 2, we move to the next smallest prime number, which is 3. Since 121 is not divisible by 3, we move to the next prime number, 5. It is also not divisible by 5. Now we try 7 and also find that it does not work. -
Check for 11
Next, we test 11.
$$ 121 \div 11 = 11 $$ -
Final Division
Since we have 11 left, and 11 is a prime number, we can write:
$$ 11 \div 11 = 1 $$ -
Writing the Prime Factorization
Now that we have reached 1, we can express the prime factorization of 484 as a product of the prime factors identified:
$$ 484 = 2^2 \times 11^2 $$
The prime factorization of 484 is ( 2^2 \times 11^2 ).
More Information
The prime factorization expresses a number in terms of its prime components, which can be useful in various mathematical applications, including finding greatest common divisors and simplifying fractions.
Tips
- Forgetting to check divisibility by smaller prime numbers before moving to larger ones.
- Not realizing that prime numbers can be repeated in the factorization (e.g., ( 11 \times 11 )).
- Confusing the order of operations; ensure to divide completely until arriving at primes.
