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Last updated on December 2nd, 2024

Is 413 a Prime Number?

Q: What are the prime factors of 413?

The prime factor of 413 is 7 and 59, when these numbers are multiplied the product will be 413. 7 x 59 = 413.

Q: What is the GCF of 413 and 777?

The GCF or greatest common factor of 413 and 777 is 7, as 7 can be used to divide both the numbers without leaving any remainder.

Q: What is the cube root of 413?

The cube root of 413 is the inverse of cubing 413 and the cube root of 413 is 7.447.

Q: What are the two square roots of 413?

The two square roots of 413 are the positive part and the negative part of the square root of 413. The square root of 413 is 20.322 and -20.322.

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A number is classified as a prime number if it satisfies a certain condition. The number has to be having only two factors 1 and the number itself, all other numbers which have more than two factors are categorized under composite numbers. The prime are used in our everyday life for the security and pin encryption and in machinery building.

Is 413 a prime number?

A prime number should not have factors more than 2 but 413 has 4 divisors. No, 413 is a composite number.

The divisors of 413 are 1, 7, 59, and 413. Therefore, 413 is a composite number. Composite numbers are the numbers which have factors more than 2.

$is 413 a prime number$

Why is 413 a prime number?

A number to be a prime number should follow the criteria, which is that it should not have factors more than 2. 413 has factors more than 2, so it is a composite number.

Given below are a few ways that can be used to find prime or composite numbers.

Using the Counting Divisors Method

In this method, the divisors of a number are listed, and the number is checked, to be called a prime number. The counting divisors method for 413 would simply be

Divisors of 413 = 1, 7, 59, 413

Number of divisors = 4

The number 413 can be considered composite.

Using the Divisibility Test Method

In divisibility method, the prime number only has 2 divisors, which are 1 and itself.

Divisors of 413 = 1, 7, 59, 413

As 413 has factors more than 2 then it is not a prime number.

Using Prime Number Chart

We write the prime number chart up to 10, which helps in sorting numbers.

The prime numbers from 400 to 500 are 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499. 413 is not on the list, so it is not a prime number.

Using the Prime Factorization Method

This method is only used for a composite number. Since 413 is a composite number, prime factorization for 413 is :

7¹ x 59¹

Hence, the prime factors of 413 are 7 and 59.

Common Mistakes to Avoid When Determining if 413 is a Prime Number.

FAQs for “Is 413 a Prime Number”?

1. What are the prime factors of 413?

2.What is the GCF of 413 and 777?

3. What is the cube root of 413?

4.What are the two square roots of 413?

Important Glossaries for "Is 413 a Prime Number"

Divisibility: The property of a number which can divide another number completely without leaving any remainder.

Chart of Prime Numbers: The numbers which has only two factors are listed together.

Composite Number: A number that has more than two positive divisors which are opposite to prime numbers which has only two factors.

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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.