Is 167 a prime number? What are the divisors of 167?

Is 167 a prime number?

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

For 167, the answer is: yes, 167 is a prime number because it has only two distinct divisors: 1 and itself (167).

As a consequence, 167 is only a multiple of 1 and 167..

Since 167 is a prime number, 167 is also a deficient number, that is to say 167 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 167 without 167 itself (that is 1, by definition!).

Parity of 167

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

Is 167 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 167 is about 12.923.

Thus, the square root of 167 is not an integer, and therefore 167 is not a square number.

Anyway, 167 is a prime number, and a prime number cannot be a perfect square.

What is the square number of 167?

The square of a number (here 167) is the result of the product of this number (167) by itself (i.e., 167 × 167); the square of 167 is sometimes called "raising 167 to the power 2", or "167 squared".

The square of 167 is 27 889 because 167 × 167 = 1672 = 27 889.

As a consequence, 167 is the square root of 27 889.

Number of digits of 167

167 is a number with 3 digits.

What are the multiples of 167?

The multiples of 167 are all integers evenly divisible by 167, that is all numbers such that the remainder of the division by 167 is zero. There are infinitely many multiples of 167. The smallest multiples of 167 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 167 too, since 0 × 167 = 0
  • 167: indeed, 167 is a multiple of itself, since 167 is evenly divisible by 167 (we have 167 / 167 = 1, so the remainder of this division is indeed zero)
  • 334: indeed, 334 = 167 × 2
  • 501: indeed, 501 = 167 × 3
  • 668: indeed, 668 = 167 × 4
  • 835: indeed, 835 = 167 × 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 167). 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 12.923). 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 167

  • Preceding numbers: …165, 166
  • Following numbers: 168, 169

Nearest numbers from 167

  • Preceding prime number: 163
  • Following prime number: 173
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