Is 1601 a prime number? What are the divisors of 1601?

## Is 1601 a prime number?

Yes, 1601 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 1601, the only two divisors are 1 and 1601. Therefore 1601 is a prime number.

As a consequence, 1601 is only a multiple of 1 and 1601.

Since 1601 is a prime number, 1601 is also a deficient number, that is to say 1601 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 1601 without 1601 itself (that is 1, by definition!).

## Parity of 1601

1601 is an odd number, because it is not evenly divisible by 2.

## Is 1601 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 1601 is about 40.012.

Thus, the square root of 1601 is not an integer, and therefore 1601 is not a square number.

Anyway, 1601 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 1601?

The square of a number (here 1601) is the result of the product of this number (1601) by itself (i.e., 1601 × 1601); the square of 1601 is sometimes called "raising 1601 to the power 2", or "1601 squared".

The square of 1601 is 2 563 201 because 1601 × 1601 = 16012 = 2 563 201.

As a consequence, 1601 is the square root of 2 563 201.

## Number of digits of 1601

1601 is a number with 4 digits.

## What are the multiples of 1601?

The multiples of 1601 are all integers evenly divisible by 1601, that is all numbers such that the remainder of the division by 1601 is zero. There are infinitely many multiples of 1601. The smallest multiples of 1601 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 1601 too, since 0 × 1601 = 0
• 1601: indeed, 1601 is a multiple of itself, since 1601 is evenly divisible by 1601 (we have 1601 / 1601 = 1, so the remainder of this division is indeed zero)
• 3 202: indeed, 3 202 = 1601 × 2
• 4 803: indeed, 4 803 = 1601 × 3
• 6 404: indeed, 6 404 = 1601 × 4
• 8 005: indeed, 8 005 = 1601 × 5
• etc.

## Nearest numbers from 1601

Find out whether some integer is a prime number