Find the prime factorization of the number 98. One of the prime factors is missing from the following list: 2, 7 What is the missing prime factor?
The Correct Answer and Explanation is:
To find the prime factorization of 98, we first divide it by the smallest prime factor, which is 2, since 98 is an even number.
Step 1: Divide 98 by 2:
98÷2=4998 \div 2 = 4998÷2=49
Now we need to factor 49. Since 49 is not divisible by 2 (it is odd), we move to the next smallest prime number, which is 7.
Step 2: Divide 49 by 7:
49÷7=749 \div 7 = 749÷7=7
At this point, we have another 7, which is a prime number, and we know that 7 cannot be divided further by any prime factor.
Step 3: Conclusion
So, the prime factorization of 98 is:
98=2×7×798 = 2 \times 7 \times 798=2×7×7
or
98=2×7298 = 2 \times 7^298=2×72
Answer: The missing prime factor in the given list (2, 7) is 7, because 49 is made up of two factors of 7.
Explanation: The process of prime factorization involves breaking a number down into prime numbers that multiply together to give the original number. The first prime factor of 98 is 2, and once we divide 98 by 2, we are left with 49. The next prime factor is 7, and since 49 is 7 multiplied by 7, we arrive at the prime factorization 98=2×7298 = 2 \times 7^298=2×72. The number 7 appears twice in this process, confirming it as the missing prime factor in the list provided.
