Is 1801 a prime number? What are the divisors of 1801?

## Is 1801 a prime number?

Yes, 1801 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 1801, the only two divisors are 1 and 1801. Therefore 1801 is a prime number.

As a consequence, 1801 is only a multiple of 1 and 1801.

Therefore year 1801 was a prime year.

Since 1801 is a prime number, 1801 is also a deficient number, that is to say 1801 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 1801 without 1801 itself (that is 1, by definition!).

## Parity of 1801

1801 is an odd number, because it is not evenly divisible by 2.

## Is 1801 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 1801 is about 42.438.

Thus, the square root of 1801 is not an integer, and therefore 1801 is not a square number.

Anyway, 1801 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 1801?

The square of a number (here 1801) is the result of the product of this number (1801) by itself (i.e., 1801 × 1801); the square of 1801 is sometimes called "raising 1801 to the power 2", or "1801 squared".

The square of 1801 is 3 243 601 because 1801 × 1801 = 18012 = 3 243 601.

As a consequence, 1801 is the square root of 3 243 601.

## Number of digits of 1801

1801 is a number with 4 digits.

## What are the multiples of 1801?

The multiples of 1801 are all integers evenly divisible by 1801, that is all numbers such that the remainder of the division by 1801 is zero. There are infinitely many multiples of 1801. The smallest multiples of 1801 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 1801 too, since 0 × 1801 = 0
• 1801: indeed, 1801 is a multiple of itself, since 1801 is evenly divisible by 1801 (we have 1801 / 1801 = 1, so the remainder of this division is indeed zero)
• 3 602: indeed, 3 602 = 1801 × 2
• 5 403: indeed, 5 403 = 1801 × 3
• 7 204: indeed, 7 204 = 1801 × 4
• 9 005: indeed, 9 005 = 1801 × 5
• etc.

## Nearest numbers from 1801

Find out whether some integer is a prime number