What is the prime factorization of 133?
Understand the Problem
The question is asking for the prime factorization of the number 133, which involves finding the prime numbers that multiply together to give the original number.
Answer
$7 \times 19$
Answer for screen readers
The prime factorization of 133 is $7 \times 19$.
Steps to Solve
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Divide by the smallest prime number
Start with the smallest prime number, which is 2. Since 133 is an odd number, it cannot be divided by 2. -
Next prime number: 3
Next, check if 3 is a factor of 133. The sum of the digits in 133 is $1 + 3 + 3 = 7$, which is not divisible by 3. Thus, 3 is not a factor. -
Check the next prime number: 5
Since 133 does not end in 0 or 5, it is not divisible by 5. -
Check the next prime number: 7
Now, divide 133 by 7.
$$ 133 \div 7 \approx 19 $$ Since 19 isn't a whole number, 7 is not a factor. We will try the next prime number. -
Check the next prime number: 11
Now, let's divide 133 by 11.
$$ 133 \div 11 \approx 12.09 $$ Since this is not an integer, 11 is not a factor. -
Check the next prime number: 13
Now try 13:
$$ 133 \div 13 = 10.23 $$ Again, this is not an integer, so 13 is also not a factor. -
Check the next prime number: 17
Finally, let's try 17:
$$ 133 \div 17 = 7.82 $$ This also is not an integer. -
Check the next prime number: 19
Calculating the division of 133 by 19:
$$ 133 \div 19 = 7 $$ This time, it works out perfectly! -
Listing the factors
Now that we have 19 and 7 as factors, we write this as:
$$ 133 = 7 \times 19 $$ -
Confirm prime factors
Both 7 and 19 are prime numbers, confirming the prime factorization of 133 is complete.
The prime factorization of 133 is $7 \times 19$.
More Information
The number 133 is interesting because it is the product of two prime numbers, making it a semiprime. Understanding prime factorization is essential in many areas of mathematics, including number theory and cryptography.
Tips
A common mistake is attempting to divide 133 by prime numbers without checking if it forms a whole number, which may lead to overlooking potential factors.
