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143 LearnersLast updated on December 24th, 2024
Is 9409 a prime number?
Prime numbers have only 1 and the number itself as factors. They are used in digital security and in securing digital payments. The topics below will help you gain more knowledge on prime numbers and how they are categorized.
Is 9409 a prime number?
The number 9409 has more than 2 factors, which means it is not a prime number. The factors of 9409 include 1, 97, and 9409.
Why is 9409 not a prime number?
For a number to be a prime number, it should have exactly 2 factors: 1 and itself. Since 9409 has more than 2 factors, it is classified as a composite number. Below are a few methods that can be used to determine whether a number is prime or composite.
The different methods we can use to check if a number is a prime number are explained below:
- Counting Divisors Method
- Divisibility Test
- Prime Number Chart
- Prime Factorization
Using the Counting Divisors Method
In the counting divisors method, we check whether the number is divisible by any numbers other than 1 and itself.
The counting divisors method for 9409 is as follows:
Divisors of 9409: 1, 97, 9409
Number of divisors: 3
The number 9409 is composite because it has more than 2 divisors.
Using the Divisibility test Method
In the divisibility test, we try to divide the number by prime numbers. If the number is divisible by any prime number other than 1 and itself, it is considered composite.
For 9409, it is divisible by 97, as:
9409 ÷ 97 = 97
Thus, 9409 is a composite number because it has more than 2 factors.
Using the Prime Number Chart
The prime number chart is a list of prime numbers starting from 2 to infinity.
The list of prime numbers under 100 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Since 9409 is not present in the list and is divisible by 97, it is not a prime number.
Using the Prime Factorization Method
This method is used only for composite numbers. Since 9409 is composite, its prime factorization is:
Factors of 9409 = 97 × 97
Common mistakes to avoid when determining if 9409 is a prime number
FAQs: "Is 9409 a prime number?"
1.What is the largest prime factor of 9409?
2.What is the smallest prime factor of 9409?
3.Is 9409 a composite number?
4.Represent 9409 in the prime factor tree?
5.Do any perfect cubes exist in the prime factors of 9409?
6.What can 9409 be divided by?
7.Do any perfect squares exist in the prime factors of 9409?
Important Glossaries for "Is 9409 a Prime Number"
- Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers.
- Composite Number: A natural number greater than 1 that has more than two distinct positive divisors. For example, 4, 6, and 9 are composite numbers.
- Divisibility: The property of a number being evenly divisible by another number, without leaving a remainder. For example, 9409 is divisible by 97 because 9409÷97=97.
- Prime Factorization: The process of expressing a composite number as a product of its prime factors. For example, the prime factorization of 9409 is 97×97.
- Perfect Square: A number that is the square of an integer. For example, 9409 is a perfect square because 97×97=9409.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
