# Is 409 a Prime Number?

Is 409 a prime number? If a number has only two factors, i.e. 1 and the number itself, it is known as a prime number. In contrast, composite numbers have more than two factors. By this explanation, can we answer the question - is 409 a prime number? According to the definition mentioned above, we can say * "yes, 409 is a prime number."* Now let us take a look at the detailed solution of why is 409 a prime number?

**Is 409 a prime number? -**Yes**Is 409 a composite number? -**No**Factors of 409 -**1, 409**Is 409 a perfect square? -**No**Prime Factors of 409 -**409

## Is 409 a Prime Number?

Yes, 409 is a prime number. The number 409 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 409 has exactly two factors, i.e. 1 and 409, it is a prime number.

## How is 409 a Prime Number?

To understand whether 409 is composite or prime, it is important to find its factors.

**Factors of 409:** 1, 409

Therefore, we can say that 409 is a prime number since it has only 2 factors.

## Is 409 a Composite Number?

No, since 409 has only two factors, i.e. 1 and 409. In other words, 409 is not a composite number because 409 doesn’t have more than 2 factors.

**Problem Statements: **

Is 409 a Prime Number? | Yes |

Is 409 a Composite Number? | No |

Is 409 a Perfect Square? | No |

Is 409 an Odd Number? | Yes |

Cube Root of 409 | 7.422899 |

Is 409 an Even Number? | No |

Square Root of 409 | 20.223748 |

Is 409 a Perfect Cube? | No |

Multiples of 409 | 409, 818, 1227, 1636, 2045, 2454, 2863, 3272, 3681, 4090 |

**Fun Facts: **

- A pair of prime numbers X and Y are said to be twin prime numbers if the absolute difference between them is 2. Example - (41, 43) are twin prime numbers.
- Euler discovered a polynomial n
^{2}+ n + 41 that produces prime numbers for values of n that lie between 0 and 39 inclusive. It can generate 40 prime numbers for 0 <= n <= 39. - All primes except 2 are odd.

**☛ Also Check: **

- Is 529 a Prime Number? - No
- Is 427 a Prime Number? - No
- Is 20 a Prime Number? - No
- Is 171 a Prime Number? - No
- Is 127 a Prime Number? - Yes
- Is 31 a Prime Number? - Yes
- Is 731 a Prime Number? - No
- Is 223 a Prime Number? - Yes

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