Is 4007 a prime number? What are the divisors of 4007?

Is 4007 a prime number?

Yes, 4007 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 4007, the only two divisors are 1 and 4007. Therefore 4007 is a prime number.

As a consequence, 4007 is only a multiple of 1 and 4007.

Since 4007 is a prime number, 4007 is also a deficient number, that is to say 4007 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 4007 without 4007 itself (that is 1, by definition!).

Parity of 4007

4007 is an odd number, because it is not evenly divisible by 2.

Is 4007 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 4007 is about 63.301.

Thus, the square root of 4007 is not an integer, and therefore 4007 is not a square number.

Anyway, 4007 is a prime number, and a prime number cannot be a perfect square.

What is the square number of 4007?

The square of a number (here 4007) is the result of the product of this number (4007) by itself (i.e., 4007 × 4007); the square of 4007 is sometimes called "raising 4007 to the power 2", or "4007 squared".

The square of 4007 is 16 056 049 because 4007 × 4007 = 40072 = 16 056 049.

As a consequence, 4007 is the square root of 16 056 049.

Number of digits of 4007

4007 is a number with 4 digits.

What are the multiples of 4007?

The multiples of 4007 are all integers evenly divisible by 4007, that is all numbers such that the remainder of the division by 4007 is zero. There are infinitely many multiples of 4007. The smallest multiples of 4007 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 4007 too, since 0 × 4007 = 0
  • 4007: indeed, 4007 is a multiple of itself, since 4007 is evenly divisible by 4007 (we have 4007 / 4007 = 1, so the remainder of this division is indeed zero)
  • 8 014: indeed, 8 014 = 4007 × 2
  • 12 021: indeed, 12 021 = 4007 × 3
  • 16 028: indeed, 16 028 = 4007 × 4
  • 20 035: indeed, 20 035 = 4007 × 5
  • etc.

Numbers near 4007

Nearest numbers from 4007

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