Write 48 as a product of prime factors.
Understand the Problem
The question is asking for the prime factorization of the number 48. This involves breaking down the number into its prime components, which are numbers greater than 1 that have no positive divisors other than 1 and themselves.
Answer
The prime factorization of 48 is $2^4 \times 3^1$.
Answer for screen readers
The prime factorization of 48 is $2^4 \times 3^1$.
Steps to Solve
- Start with the number
We need to factor the number 48. Start by dividing it by the smallest prime number, which is 2.
- Divide by the smallest prime number
$$ 48 \div 2 = 24 $$
Now we have 24. Keep dividing by 2.
- Continue dividing by 2
$$ 24 \div 2 = 12 $$
Next, divide 12 by 2.
- Repeat the process
$$ 12 \div 2 = 6 $$
Now, divide 6 by 2 again.
- Final division by 2
$$ 6 \div 2 = 3 $$
At this point, we cannot divide by 2 anymore, so we look for the next prime number, which is 3.
- Check if it's prime
The last quotient is 3, which is a prime number.
- Write out the prime factorization
Now we can write the prime factorization of 48:
$$ 48 = 2^4 \times 3^1 $$
This shows that 48 is made up of four 2's and one 3.
The prime factorization of 48 is $2^4 \times 3^1$.
More Information
The prime factorization helps in understanding the fundamental building blocks of a number. In this case, since 48 is even, we were able to divide by 2 multiple times until we reached a prime number, which shows how easily even numbers can be factored into smaller primes.
Tips
- Dividing by incorrect numbers: Sometimes people forget to only divide by prime numbers. Ensure you are using primes like 2, 3, 5, etc.
- Stopping too early: Make sure to continue factoring until you reach a prime number that cannot be divided further.
