Introduction :
In this we will study about number theory research. Number theory research is one of the most olden areas of research in math. Number theory is a study of all types of numbers in math such as integers, whole number, and so on. Let us start our research in number theory.
Example Problems for Number Theory Research:
Example problem 1: How do you write 88,000 in scientific notation?
Solution:
Shift the decimal point to the left until the number is between 1 and 10. Calculate the places we move the decimal point.
88,000 ? 8.8
We moved the decimal point 4 places to the left. The power of 10 is 104.
88,000 = 8.8 × 104
Answer: 88,000 = 8.8 × 104
Example problem 2: Which of the following numbers are primes?
5, 18,17, 8
Solution:
The factors of 5 are 1 and 5. Since the only factors of 5 are 1 and itself, 5 is prime number.
The factors of 18 are given as1, 2, 3, 6, 9, and 18. Since 18 has more factors than just 1 and itself, 18 is not prime number.
The factors of 17 are given as 1 and 17. Since the only factors of 17 are 1 and itself, 17 is prime number.
The factors of 8 are given as1, 2, 4, and 8. Since 8 has more factors than just 1 and itself, 8 is not prime number.
Therefore, the prime numbers are 5 and 17.
Answer: The prime numbers are 5 and 17.
Practice Problems for Number Theory Research:
Practice problem 1: Which number is prime number? 20, 7, 16, 10
Practice problem 2: What is the prime factorization of 16?
Practice problem 3: Write is the greatest common factor of 10 and 6.
Solutions for number theory research:
Solution 1: The prime number is 7.
Solution 2: The prime factorization of 16 is 2 * 2* 2* 2.
Solution 3: The greatest common factor of 10 and 6 is 2.
In this we will study about number theory research. Number theory research is one of the most olden areas of research in math. Number theory is a study of all types of numbers in math such as integers, whole number, and so on. Let us start our research in number theory.
Example Problems for Number Theory Research:
Example problem 1: How do you write 88,000 in scientific notation?
Solution:
Shift the decimal point to the left until the number is between 1 and 10. Calculate the places we move the decimal point.
88,000 ? 8.8
We moved the decimal point 4 places to the left. The power of 10 is 104.
88,000 = 8.8 × 104
Answer: 88,000 = 8.8 × 104
Example problem 2: Which of the following numbers are primes?
5, 18,17, 8
Solution:
The factors of 5 are 1 and 5. Since the only factors of 5 are 1 and itself, 5 is prime number.
The factors of 18 are given as1, 2, 3, 6, 9, and 18. Since 18 has more factors than just 1 and itself, 18 is not prime number.
The factors of 17 are given as 1 and 17. Since the only factors of 17 are 1 and itself, 17 is prime number.
The factors of 8 are given as1, 2, 4, and 8. Since 8 has more factors than just 1 and itself, 8 is not prime number.
Therefore, the prime numbers are 5 and 17.
Answer: The prime numbers are 5 and 17.
Practice Problems for Number Theory Research:
Practice problem 1: Which number is prime number? 20, 7, 16, 10
Practice problem 2: What is the prime factorization of 16?
Practice problem 3: Write is the greatest common factor of 10 and 6.
Solutions for number theory research:
Solution 1: The prime number is 7.
Solution 2: The prime factorization of 16 is 2 * 2* 2* 2.
Solution 3: The greatest common factor of 10 and 6 is 2.
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