Is 10007 a prime number? What are the divisors of 10007?

## Is 10007 a prime number?

Yes, 10007 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 10007, the only two divisors are 1 and 10007. Therefore 10007 is a prime number.

As a consequence, 10007 is only a multiple of 1 and 10007.

Since 10007 is a prime number, 10007 is also a deficient number, that is to say 10007 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 10007 without 10007 itself (that is 1, by definition!).

## Parity of 10007

10007 is an odd number, because it is not evenly divisible by 2.

## Is 10007 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 10007 is about 100.035.

Thus, the square root of 10007 is not an integer, and therefore 10007 is not a square number.

Anyway, 10007 is a prime number, and a prime number cannot be a perfect square.

## What is the square number of 10007?

The square of a number (here 10007) is the result of the product of this number (10007) by itself (i.e., 10007 × 10007); the square of 10007 is sometimes called "raising 10007 to the power 2", or "10007 squared".

The square of 10007 is 100 140 049 because 10007 × 10007 = 100072 = 100 140 049.

As a consequence, 10007 is the square root of 100 140 049.

## Number of digits of 10007

10007 is a number with 5 digits.

## What are the multiples of 10007?

The multiples of 10007 are all integers evenly divisible by 10007, that is all numbers such that the remainder of the division by 10007 is zero. There are infinitely many multiples of 10007. The smallest multiples of 10007 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 10007 too, since 0 × 10007 = 0
• 10007: indeed, 10007 is a multiple of itself, since 10007 is evenly divisible by 10007 (we have 10007 / 10007 = 1, so the remainder of this division is indeed zero)
• 20 014: indeed, 20 014 = 10007 × 2
• 30 021: indeed, 30 021 = 10007 × 3
• 40 028: indeed, 40 028 = 10007 × 4
• 50 035: indeed, 50 035 = 10007 × 5
• etc.

## Nearest numbers from 10007

Find out whether some integer is a prime number