Is 165 a prime number?

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

For 165, the answer is: No, 165 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 165) is as follows: 1, 3, 5, 11, 15, 33, 55, 165.

For 165 to be a prime number, it would have been required that 165 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 165 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 165 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

165 is a multiple of 1
165 is a multiple of 3
165 is a multiple of 5
165 is a multiple of 11
165 is a multiple of 15
165 is a multiple of 33
165 is a multiple of 55

For 165 to be a prime number, it would have been required that 165 has only two divisors, i.e., itself and 1.

Is 165 a deficient number?

Yes, 165 is a deficient number, that is to say 165 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 165 without 165 itself (that is 1 + 3 + 5 + 11 + 15 + 33 + 55 = 123).

Parity of 165

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

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What is an even number?

Is 165 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 165 is about 12.845.

Thus, the square root of 165 is not an integer, and therefore 165 is not a square number.

What is the square number of 165?

The square of a number (here 165) is the result of the product of this number (165) by itself (i.e., 165 × 165); the square of 165 is sometimes called "raising 165 to the power 2", or "165 squared".

The square of 165 is 27 225 because 165 × 165 = 165² = 27 225.

As a consequence, 165 is the square root of 27 225.

Number of digits of 165

165 is a number with 3 digits.

What are the multiples of 165?

The multiples of 165 are all integers evenly divisible by 165, that is all numbers such that the remainder of the division by 165 is zero. There are infinitely many multiples of 165. The smallest multiples of 165 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 165 too, since 0 × 165 = 0
165: indeed, 165 is a multiple of itself, since 165 is evenly divisible by 165 (we have 165 / 165 = 1, so the remainder of this division is indeed zero)
330: indeed, 330 = 165 × 2
495: indeed, 495 = 165 × 3
660: indeed, 660 = 165 × 4
825: indeed, 825 = 165 × 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 165). 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 12.845). 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 165

Preceding numbers: …163, 164
Following numbers: 166, 167…

Nearest numbers from 165

Preceding prime number: 163
Following prime number: 167