Write 88 as a product of prime factors.
Understand the Problem
The question is asking how to express the number 88 as a product of its prime factors. To solve this, we will find the prime numbers that multiply together to give 88.
Answer
The prime factorization of 88 is $2^3 \times 11$.
Answer for screen readers
The prime factorization of 88 is $2^3 \times 11$.
Steps to Solve
- Start with the number 88
Begin by identifying the number you need to factor, which is 88.
- Divide by the smallest prime number
Start dividing 88 by the smallest prime number, which is 2.
$$ 88 \div 2 = 44 $$
- Repeat the division
Continue dividing the result by 2 as long as it remains even.
$$ 44 \div 2 = 22 $$
$$ 22 \div 2 = 11 $$
- Identify the next prime number
Now that you have 11, which is a prime number, you cannot divide it further by 2. Instead, you check the next prime number, which is 3.
Since 11 cannot be divided by 3, move on to the next prime number, which is 5. The number 11 is also not divisible by 5.
- Conclude the factoring process
Since 11 is a prime number, we can conclude that the complete factorization of 88 in terms of its prime factors is:
$$ 88 = 2^3 \times 11 $$
The prime factorization of 88 is $2^3 \times 11$.
More Information
Prime factorization breaks down a number into the set of prime numbers that multiply together to create the original number. The process of finding prime factors is important in many areas of mathematics, including number theory and algebra.
Tips
- Forgetting to check for divisibility by smaller prime numbers before moving on to larger ones.
- Overlooking the fact that if a number is a prime, it cannot be divided by any prime numbers other than itself and one.
