Write 98 as a product of prime factors.
Understand the Problem
The question is asking to express the number 98 as a product of its prime factors. This will involve identifying the prime numbers that can be multiplied together to yield 98.
Answer
The prime factorization of 98 is $2 \times 7^2$.
Answer for screen readers
The prime factorization of 98 is $2 \times 7^2$.
Steps to Solve
- Start with the number 98
Begin the factorization process by dividing 98 by the smallest prime number, which is 2.
$$ 98 \div 2 = 49 $$
- Factor 49
Now, we have 49. The next step is to factor 49, which is not divisible by 2 (since it's odd). The next prime number is 3, but 49 is not divisible by 3. We check the next prime, which is 5, but 49 is also not divisible by 5. We continue to the next prime number, which is 7.
$$ 49 \div 7 = 7 $$
- Continue factoring
We have now reached a factor of 7, and since 7 is a prime number, we can stop here.
Therefore, we have: $$ 49 = 7 \times 7 $$
- Combine the factors
Putting it all together, we have: $$ 98 = 2 \times 7 \times 7 $$
We can also write this using exponents for the repeated factor: $$ 98 = 2 \times 7^2 $$
The prime factorization of 98 is $2 \times 7^2$.
More Information
The prime factorization process helps break down a composite number into the prime numbers that multiply together to form it. Prime factorization is useful in various areas of mathematics, such as simplifying fractions and finding least common multiples.
Tips
One common mistake is forgetting to continue factoring until only prime numbers are left. Make sure to always check if your factors are prime after dividing.
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