Write 98 as a product of its prime factors.

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2 \times 3^{2}

2 \times 3^{3}

2 \times 7^{2}

2^{2} \times 5^{2}

answer is B.

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Detailed Solution

The given number is 98. To express 98 as a product of its prime factors, we will perform its prime factorization step-by-step:

Step-by-Step Prime Factorization of 98

Start by dividing the number 98 by the smallest prime number, which is 2, since 98 is even.
98 ÷ 2 = 49. Thus, 2 is one of the factors of 98.
Next, take the quotient 49 and divide it by the smallest prime number that evenly divides it. Since 49 is not divisible by 2, we try the next prime number, 7.
49 ÷ 7 = 7. Thus, 7 is another factor of 98.
Finally, divide 7 by 7 to get 1. Since the quotient is 1, we stop here.

Conclusion

The prime factorization of 98 is:

98 = 2 × 7 × 7

Alternatively, it can also be expressed as:

98 = 2 × 7²

Hence, the prime factors of 98 are 2 and 7. The factors of 98 in terms of prime factorization clearly demonstrate that 98 is composed of these prime numbers.

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