Is 1009 a prime number? What are the divisors of 1009?

## Is 1009 a prime number?

Yes, 1009 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 1009, the only two divisors are 1 and 1009. Therefore 1009 is a prime number.

As a consequence, 1009 is only a multiple of 1 and 1009.

Since 1009 is a prime number, 1009 is also a deficient number, that is to say 1009 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 1009 without 1009 itself (that is 1, by definition!).

## Parity of 1009

1009 is an odd number, because it is not evenly divisible by 2.

## Is 1009 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 1009 is about 31.765.

Thus, the square root of 1009 is not an integer, and therefore 1009 is not a square number.

Anyway, 1009 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 1009?

The square of a number (here 1009) is the result of the product of this number (1009) by itself (i.e., 1009 × 1009); the square of 1009 is sometimes called "raising 1009 to the power 2", or "1009 squared".

The square of 1009 is 1 018 081 because 1009 × 1009 = 10092 = 1 018 081.

As a consequence, 1009 is the square root of 1 018 081.

## Number of digits of 1009

1009 is a number with 4 digits.

## What are the multiples of 1009?

The multiples of 1009 are all integers evenly divisible by 1009, that is all numbers such that the remainder of the division by 1009 is zero. There are infinitely many multiples of 1009. The smallest multiples of 1009 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 1009 too, since 0 × 1009 = 0
• 1009: indeed, 1009 is a multiple of itself, since 1009 is evenly divisible by 1009 (we have 1009 / 1009 = 1, so the remainder of this division is indeed zero)
• 2 018: indeed, 2 018 = 1009 × 2
• 3 027: indeed, 3 027 = 1009 × 3
• 4 036: indeed, 4 036 = 1009 × 4
• 5 045: indeed, 5 045 = 1009 × 5
• etc.

## Nearest numbers from 1009

• Preceding prime number: 997
• Following prime number: 1 013
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