Prime factorization of 182
Understand the Problem
The question is asking for the prime factors of the number 182. To solve this, we will divide the number 182 by the smallest prime numbers and continue the process with the resulting quotients until we reach a quotient of 1.
Answer
The prime factors of 182 are $2$, $7$, and $13$.
Answer for screen readers
The prime factors of 182 are $2$, $7$, and $13$.
Steps to Solve
- Start with the number 182
Begin by identifying the smallest prime number to test as a factor of 182. The smallest prime number is 2.
- Divide by 2
Since 182 is even, we can divide it by 2:
$$ 182 \div 2 = 91 $$
Now we have 91 as the quotient.
- Test the next smallest prime number
Next, we check if 91 can be divided by 2. It cannot since it’s odd. The next smallest prime to check is 3.
$$ 91 \div 3 \neq \text{integer} \quad (\text{since } 91 \div 3 = 30.33) $$
- Continue with the next prime number, 5
Since 91 is not divisible by 3, we check 5:
$$ 91 \div 5 \neq \text{integer} \quad (\text{since } 91 \div 5 = 18.2) $$
- Check against the next prime, 7
Now, we check 7:
$$ 91 \div 7 = 13 $$
Thus, 7 is a factor, and we have a quotient of 13.
- Prime factor check for 13
Now we need to check if 13 is a prime number. It has no divisors other than 1 and 13 itself, so 13 is prime.
- Combine the prime factors
The prime factors of 182 can now be expressed as:
$$ 182 = 2 \times 7 \times 13 $$
The prime factors of 182 are $2$, $7$, and $13$.
More Information
Prime factorization is the process of determining the prime numbers that multiply together to give a specific integer. This is foundational in number theory and can be useful in areas such as computing and cryptography.
Tips
- Mistaking a composite number for a prime number; always double-check if a number has additional factors.
- Overlooking larger primes; continue checking prime numbers until the quotient reaches 1.
