Is 1409 a prime number? What are the divisors of 1409?

## Is 1409 a prime number?

Yes, 1409 is a prime number.

Indeed, the definition of a prime numbers is to have only two distinct positive divisors, 1 and itself. A number is a divisor of another number when the remainder of Euclid’s division of the second one by the first one is zero. Concerning the number 1409, the only two divisors are 1 and 1409. Therefore 1409 is a prime number.

As a consequence, 1409 is only a multiple of 1 and 1409.

Since 1409 is a prime number, 1409 is also a deficient number, that is to say 1409 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 1409 without 1409 itself (that is 1, by definition!).

## Parity of 1409

1409 is an odd number, because it is not evenly divisible by 2.

## Is 1409 a perfect square number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 1409 is about 37.537.

Thus, the square root of 1409 is not an integer, and therefore 1409 is not a square number.

Anyway, 1409 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 1409?

The square of a number (here 1409) is the result of the product of this number (1409) by itself (i.e., 1409 × 1409); the square of 1409 is sometimes called "raising 1409 to the power 2", or "1409 squared".

The square of 1409 is 1 985 281 because 1409 × 1409 = 14092 = 1 985 281.

As a consequence, 1409 is the square root of 1 985 281.

## Number of digits of 1409

1409 is a number with 4 digits.

## What are the multiples of 1409?

The multiples of 1409 are all integers evenly divisible by 1409, that is all numbers such that the remainder of the division by 1409 is zero. There are infinitely many multiples of 1409. The smallest multiples of 1409 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 1409 too, since 0 × 1409 = 0
• 1409: indeed, 1409 is a multiple of itself, since 1409 is evenly divisible by 1409 (we have 1409 / 1409 = 1, so the remainder of this division is indeed zero)
• 2 818: indeed, 2 818 = 1409 × 2
• 4 227: indeed, 4 227 = 1409 × 3
• 5 636: indeed, 5 636 = 1409 × 4
• 7 045: indeed, 7 045 = 1409 × 5
• etc.

## Nearest numbers from 1409

Find out whether some integer is a prime number