165 LearnersLast updated on May 26th, 2025
Is 407 a Prime Number?
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 407 a prime number?
A prime number should not have factors more than 2 but 407 has 4 divisors. No, 407 is a composite number.
The divisors of 407 are1, 11, 37, and 407. Therefore, 407 is a composite number. Composite numbers are the numbers which have factors more than 2.
Why is 407 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. 407 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 407 would simply be
Divisors of 407=1, 11, 37, 407.
Number of divisors = 4
The number 407 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 407= 1, 11, 37, 407.
As 407 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. 407 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 407 is a composite number, prime factorization for 407 is : 111 × 371
Hence, the prime factors of 407 are 11 and 37.
Common Mistakes to Avoid When Determining if 407 is a Prime Number.
It is common to make mistakes while learning the prime numbers, and children while learning prime numbers for the first time it is mostly certain to happen. The mistakes and the solution given below will help you in getting an idea on where all mistakes might be made and how to avoid them.
Mistake 1
Not considering 1 as a factor.
Students might not count 1 as a factor, and will mostly skip it, which results in wrong count of factors.
FAQs for “Is 407 a Prime Number”
1.Is 407 odd or even?
2.What is 407 multiplied by 8?
3.Is 407 divisible by 7?
4.What are common number factors?
5.What is the multiple of 407?
Important Glossaries for "Is 407 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.
Fun Fact
: She loves to read number jokes and games.
