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

Is 208 a prime number?

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

For 208, the answer is: No, 208 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 208) is as follows: 1, 2, 4, 8, 13, 16, 26, 52, 104, 208.

To be 208 a prime number, it would have been required that 208 has only two divisors, i.e., itself and 1.

As a consequence:

  • 208 is a multiple of 1
  • 208 is a multiple of 2
  • 208 is a multiple of 4
  • 208 is a multiple of 8
  • 208 is a multiple of 13
  • 208 is a multiple of 16
  • 208 is a multiple of 26
  • 208 is a multiple of 52
  • 208 is a multiple of 104

To be 208 a prime number, it would have been required that 208 has only two divisors, i.e., itself and 1.

Is 208 a deficient number?

No, 208 is not a deficient number: to be deficient, 208 should have been such that 208 is larger than the sum of its proper divisors, i.e., the divisors of 208 without 208 itself (that is 1 + 2 + 4 + 8 + 13 + 16 + 26 + 52 + 104 = 226).

In fact, 208 is an abundant number; 208 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 13 + 16 + 26 + 52 + 104 = 226). The smallest abundant number is 12.

Parity of 208

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

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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