Is 1637 a prime number? What are the divisors of 1637?

## Is 1637 a prime number?

Yes, 1637 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 1637, the only two divisors are 1 and 1637. Therefore 1637 is a prime number.

As a consequence, 1637 is only a multiple of 1 and 1637.

Since 1637 is a prime number, 1637 is also a deficient number, that is to say 1637 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 1637 without 1637 itself (that is 1, by definition!).

## Parity of 1637

1637 is an odd number, because it is not evenly divisible by 2.

## Is 1637 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 1637 is about 40.460.

Thus, the square root of 1637 is not an integer, and therefore 1637 is not a square number.

Anyway, 1637 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 1637?

The square of a number (here 1637) is the result of the product of this number (1637) by itself (i.e., 1637 × 1637); the square of 1637 is sometimes called "raising 1637 to the power 2", or "1637 squared".

The square of 1637 is 2 679 769 because 1637 × 1637 = 16372 = 2 679 769.

As a consequence, 1637 is the square root of 2 679 769.

## Number of digits of 1637

1637 is a number with 4 digits.

## What are the multiples of 1637?

The multiples of 1637 are all integers evenly divisible by 1637, that is all numbers such that the remainder of the division by 1637 is zero. There are infinitely many multiples of 1637. The smallest multiples of 1637 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 1637 too, since 0 × 1637 = 0
• 1637: indeed, 1637 is a multiple of itself, since 1637 is evenly divisible by 1637 (we have 1637 / 1637 = 1, so the remainder of this division is indeed zero)
• 3 274: indeed, 3 274 = 1637 × 2
• 4 911: indeed, 4 911 = 1637 × 3
• 6 548: indeed, 6 548 = 1637 × 4
• 8 185: indeed, 8 185 = 1637 × 5
• etc.

## Nearest numbers from 1637

Find out whether some integer is a prime number