What is the prime factorization of 168?
Understand the Problem
The question is asking for the prime factorization of the number 168, which involves breaking it down into its prime factors.
Answer
The prime factorization of 168 is \( 2^3 \times 3^1 \times 7^1 \).
Answer for screen readers
The prime factorization of 168 is ( 2^3 \times 3^1 \times 7^1 ).
Steps to Solve
- Start with the number 168
Begin the factorization process by dividing 168 by the smallest prime number, which is 2.
$$ 168 \div 2 = 84 $$
- Continue dividing by 2
Since 84 is even, you can continue dividing by 2.
$$ 84 \div 2 = 42 $$
- Keep dividing by 2
As 42 is also even, divide by 2 again.
$$ 42 \div 2 = 21 $$
- Switch to the next prime number
Now, since 21 is odd, we try dividing by the next prime number, which is 3.
$$ 21 \div 3 = 7 $$
- Final division
Finally, 7 is a prime number itself, so we stop here.
The complete factorization is:
$$ 168 = 2^3 \times 3^1 \times 7^1 $$
The prime factorization of 168 is ( 2^3 \times 3^1 \times 7^1 ).
More Information
Prime factorization helps us understand the building blocks of a number, which can be useful for many mathematical applications, including finding the greatest common divisor and least common multiple.
Tips
- A common mistake is failing to continue dividing by smaller prime numbers. Ensure you check if the number is even or if it is divisible by smaller primes before moving on.
- Another mistake is miscounting the number of times you divide by a prime factor. Be diligent about keeping track of how many times each prime factor is used.
