What is the prime factorization of 80?
Understand the Problem
The question is asking for the prime factorization of the number 80. Prime factorization involves breaking down a number into its basic building blocks, which are prime numbers, that when multiplied together yield the original number. To solve this, we will find the prime numbers that multiply to give us 80.
Answer
2^4 * 5
Answer for screen readers
The prime factorization of 80 is 2^4 * 5.
Steps to Solve
- Divide by the smallest prime number (2)
Since 80 is even, we start by dividing it by the smallest prime number, which is 2.
$$ 80 \div 2 = 40 $$
- Divide the quotient by the smallest prime number (2) again
We continue dividing by 2 because 40 is also an even number.
$$ 40 \div 2 = 20 $$
- Repeat the process
Again, since 20 is even, we divide by 2.
$$ 20 \div 2 = 10 $$
- Divide by 2 one more time
10 is also even, so we divide by 2.
$$ 10 \div 2 = 5 $$
- Divide the remaining quotient (5) by the smallest prime number
5 is not divisible by 2, so we move to the next smallest prime number, which is 5.
$$ 5 \div 5 = 1 $$
Since we have reached 1, we stop. The prime factors are the numbers we used to divide.
The prime factorization of 80 is 2^4 * 5.
More Information
Prime factorization is a useful tool in many areas of number theory and can help simplify the solving of various mathematical problems.
Tips
A common mistake is to miss a prime factor or to not fully divide down to 1. Always check if the remaining quotient can be divided by the smallest prime number.
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