Is 208 a prime number? What are the divisors of 208?

Parity of 208

208 is an even number, because it is evenly divisible by 2: 208 / 2 = 104.

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Is 208 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 208 is about 14.422.

Thus, the square root of 208 is not an integer, and therefore 208 is not a square number.

What is the square number of 208?

The square of a number (here 208) is the result of the product of this number (208) by itself (i.e., 208 × 208); the square of 208 is sometimes called "raising 208 to the power 2", or "208 squared".

The square of 208 is 43 264 because 208 × 208 = 2082 = 43 264.

As a consequence, 208 is the square root of 43 264.

Number of digits of 208

208 is a number with 3 digits.

What are the multiples of 208?

The multiples of 208 are all integers evenly divisible by 208, that is all numbers such that the remainder of the division by 208 is zero. There are infinitely many multiples of 208. The smallest multiples of 208 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 208 too, since 0 × 208 = 0
  • 208: indeed, 208 is a multiple of itself, since 208 is evenly divisible by 208 (we have 208 / 208 = 1, so the remainder of this division is indeed zero)
  • 416: indeed, 416 = 208 × 2
  • 624: indeed, 624 = 208 × 3
  • 832: indeed, 832 = 208 × 4
  • 1 040: indeed, 1 040 = 208 × 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 208). 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 14.422). 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 208

  • Preceding numbers: …206, 207
  • Following numbers: 209, 210…

Nearest numbers from 208

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