What is the prime factorization of 121?
Understand the Problem
The question is asking for the prime factors of the number 121. To find the prime factorization, we need to identify the prime numbers that multiply together to result in 121.
Answer
The prime factorization of 121 is $11^2$.
Answer for screen readers
The prime factorization of 121 is $11^2$.
Steps to Solve
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Identify the smallest prime number
We start with the smallest prime number, which is 2. We need to check if 121 is divisible by 2. Since 121 is an odd number, it is not divisible by 2. -
Check the next prime number
The next prime number is 3. We check if 121 is divisible by 3 by adding the digits (1 + 2 + 1 = 4) and seeing if 4 is divisible by 3. Since it is not, 121 is not divisible by 3. -
Move to the next prime number
Next, we check the prime number 5. Since 121 does not end in 0 or 5, it is not divisible by 5. -
Check divisibility by 7
Now we check 7. Dividing 121 by 7 gives approximately 17.29, which is not an integer, so 121 is not divisible by 7. -
Check divisibility by 11
Next, we check 11. We divide 121 by 11:
$$ 121 \div 11 = 11 $$
This result is an integer, indicating that 121 is divisible by 11. -
Determine prime factors
Since we have found that 11 is a prime factor, we can express 121 as:
$$ 121 = 11 \times 11 = 11^2 $$
Thus, the prime factorization of 121 is $11^2$.
The prime factorization of 121 is $11^2$.
More Information
The number 121 is known as a perfect square because it is the square of the prime number 11. Perfect squares can be expressed as the prime number raised to an exponent.
Tips
A common mistake when finding prime factors is to stop checking once a number is found that divides evenly. It's crucial to continue testing all smaller prime numbers to ensure no factors are missed.
