Is 161 a prime number?

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

For 161, the answer is: No, 161 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 161) is as follows: 1, 7, 23, 161.

For 161 to be a prime number, it would have been required that 161 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

161 is a multiple of 1
161 is a multiple of 7
161 is a multiple of 23

For 161 to be a prime number, it would have been required that 161 has only two divisors, i.e., itself and 1.

However, 161 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 161 = 7 x 23, where 7 and 23 are both prime numbers.

Is 161 a deficient number?

Yes, 161 is a deficient number, that is to say 161 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 161 without 161 itself (that is 1 + 7 + 23 = 31).

Parity of 161

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

Find out more:

What is an even number?

Is 161 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 161 is about 12.689.

Thus, the square root of 161 is not an integer, and therefore 161 is not a square number.

What is the square number of 161?

The square of a number (here 161) is the result of the product of this number (161) by itself (i.e., 161 × 161); the square of 161 is sometimes called "raising 161 to the power 2", or "161 squared".

The square of 161 is 25 921 because 161 × 161 = 161² = 25 921.

As a consequence, 161 is the square root of 25 921.

Number of digits of 161

161 is a number with 3 digits.

What are the multiples of 161?

The multiples of 161 are all integers evenly divisible by 161, that is all numbers such that the remainder of the division by 161 is zero. There are infinitely many multiples of 161. The smallest multiples of 161 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 161 too, since 0 × 161 = 0
161: indeed, 161 is a multiple of itself, since 161 is evenly divisible by 161 (we have 161 / 161 = 1, so the remainder of this division is indeed zero)
322: indeed, 322 = 161 × 2
483: indeed, 483 = 161 × 3
644: indeed, 644 = 161 × 4
805: indeed, 805 = 161 × 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 161). 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 12.689). 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 161

Preceding numbers: …159, 160
Following numbers: 162, 163…

Nearest numbers from 161

Preceding prime number: 157
Following prime number: 163