Write 40 as a product of prime factors.
Understand the Problem
The question is asking for the prime factorization of the number 40, which means we need to express 40 as a product of its prime factors.
Answer
The prime factorization of 40 is $2^3 \times 5$.
Answer for screen readers
The prime factorization of 40 is $2^3 \times 5$.
Steps to Solve
- Start with the number 40
Begin with the number you want to factor, which is 40.
- Divide by the smallest prime number
Start dividing 40 by the smallest prime number, which is 2.
$$ 40 \div 2 = 20 $$
- Continue dividing by 2
Since 20 is still even, divide it by 2 again.
$$ 20 \div 2 = 10 $$
- Divide 10 by 2
Continue with the division by 2 as long as the quotient remains even.
$$ 10 \div 2 = 5 $$
- Factor the remaining number
Now, we have 5, which is a prime number. So we cannot divide it further by any prime except itself.
- Write the prime factorization
Combine all prime factors to write the final prime factorization of 40.
$$ 40 = 2^3 \times 5 $$
The prime factorization of 40 is $2^3 \times 5$.
More Information
Prime factorization is useful for many areas in mathematics, including simplifying fractions and finding the least common multiple (LCM) or greatest common divisor (GCD). It's also essential in number theory.
Tips
- Forgetting to check for prime factors: Sometimes, people do not continue dividing by the smallest prime until reaching a prime number.
- Miscounting prime factors: Make sure to keep track of how many times each prime number can divide the original number.
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