Is 200 a prime number? What are the divisors of 200?

Is 200 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 200, the answer is: No, 200 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 200) is as follows: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.

To be 200 a prime number, it would have been required that 200 has only two divisors, i.e., itself and 1.

As a consequence:

  • 200 is a multiple of 1
  • 200 is a multiple of 2
  • 200 is a multiple of 4
  • 200 is a multiple of 5
  • 200 is a multiple of 8
  • 200 is a multiple of 10
  • 200 is a multiple of 20
  • 200 is a multiple of 25
  • 200 is a multiple of 40
  • 200 is a multiple of 50
  • 200 is a multiple of 100

To be 200 a prime number, it would have been required that 200 has only two divisors, i.e., itself and 1.

Is 200 a deficient number?

No, 200 is not a deficient number: to be deficient, 200 should have been such that 200 is larger than the sum of its proper divisors, i.e., the divisors of 200 without 200 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 = 265).

In fact, 200 is an abundant number; 200 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 = 265). The smallest abundant number is 12.

Parity of 200

200 is an even number, because it is evenly divisible by 2: 200 / 2 = 100.

Is 200 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 200 is about 14.142.

Thus, the square root of 200 is not an integer, and therefore 200 is not a square number.

What is the square number of 200?

The square of a number (here 200) is the result of the product of this number (200) by itself (i.e., 200 × 200); the square of 200 is sometimes called "raising 200 to the power 2", or "200 squared".

The square of 200 is 40 000 because 200 × 200 = 2002 = 40 000.

As a consequence, 200 is the square root of 40 000.

Number of digits of 200

200 is a number with 3 digits.

What are the multiples of 200?

The multiples of 200 are all integers evenly divisible by 200, that is all numbers such that the remainder of the division by 200 is zero. There are infinitely many multiples of 200. The smallest multiples of 200 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 200 too, since 0 × 200 = 0
  • 200: indeed, 200 is a multiple of itself, since 200 is evenly divisible by 200 (we have 200 / 200 = 1, so the remainder of this division is indeed zero)
  • 400: indeed, 400 = 200 × 2
  • 600: indeed, 600 = 200 × 3
  • 800: indeed, 800 = 200 × 4
  • 1 000: indeed, 1 000 = 200 × 5
  • etc.

How to determine whether an integer is a prime number?

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 200). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 14.142). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

Numbers near 200

  • Preceding numbers: …198, 199
  • Following numbers: 201, 202

Nearest numbers from 200

  • Preceding prime number: 199
  • Following prime number: 211
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