Is 201 a prime number? What are the divisors of 201?

Is 201 a prime number?

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

For 201, the answer is: No, 201 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 201) is as follows: 1, 3, 67, 201.

To be 201 a prime number, it would have been required that 201 has only two divisors, i.e., itself and 1.

As a consequence:

  • 201 is a multiple of 1
  • 201 is a multiple of 3
  • 201 is a multiple of 67

To be 201 a prime number, it would have been required that 201 has only two divisors, i.e., itself and 1.

However, 201 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 201 = 3 x 67, where 3 and 67 are both prime numbers.

Is 201 a deficient number?

Yes, 201 is a deficient number, that is to say 201 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 201 without 201 itself (that is 1 + 3 + 67 = 71).

Parity of 201

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

Is 201 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 201 is about 14.177.

Thus, the square root of 201 is not an integer, and therefore 201 is not a square number.

What is the square number of 201?

The square of a number (here 201) is the result of the product of this number (201) by itself (i.e., 201 × 201); the square of 201 is sometimes called "raising 201 to the power 2", or "201 squared".

The square of 201 is 40 401 because 201 × 201 = 2012 = 40 401.

As a consequence, 201 is the square root of 40 401.

Number of digits of 201

201 is a number with 3 digits.

What are the multiples of 201?

The multiples of 201 are all integers evenly divisible by 201, that is all numbers such that the remainder of the division by 201 is zero. There are infinitely many multiples of 201. The smallest multiples of 201 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 201 too, since 0 × 201 = 0
  • 201: indeed, 201 is a multiple of itself, since 201 is evenly divisible by 201 (we have 201 / 201 = 1, so the remainder of this division is indeed zero)
  • 402: indeed, 402 = 201 × 2
  • 603: indeed, 603 = 201 × 3
  • 804: indeed, 804 = 201 × 4
  • 1 005: indeed, 1 005 = 201 × 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 201). 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 14.177). 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 201

  • Preceding numbers: …199, 200
  • Following numbers: 202, 203

Nearest numbers from 201

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