Is 961 a prime number? What are the divisors of 961?

## Is 961 a prime number?

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

For 961, the answer is: No, 961 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 961) is as follows: 1, 31, 961.

To be 961 a prime number, it would have been required that 961 has only two divisors, i.e., itself and 1.

As a consequence:

• 961 is a multiple of 1
• 961 is a multiple of 31

To be 961 a prime number, it would have been required that 961 has only two divisors, i.e., itself and 1.

However, 961 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 961 = 31 x 31, where 31 is a prime number.

## Is 961 a deficient number?

Yes, 961 is a deficient number, that is to say 961 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 961 without 961 itself (that is 1 + 31 = 32).

## Parity of 961

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

## Is 961 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 961 is 31.

Therefore, the square root of 961 is an integer, and as a consequence 961 is a perfect square.

As a consequence, 31 is the square root of 961.

## What is the square number of 961?

The square of a number (here 961) is the result of the product of this number (961) by itself (i.e., 961 × 961); the square of 961 is sometimes called "raising 961 to the power 2", or "961 squared".

The square of 961 is 923 521 because 961 × 961 = 9612 = 923 521.

As a consequence, 961 is the square root of 923 521.

## Number of digits of 961

961 is a number with 3 digits.

## What are the multiples of 961?

The multiples of 961 are all integers evenly divisible by 961, that is all numbers such that the remainder of the division by 961 is zero. There are infinitely many multiples of 961. The smallest multiples of 961 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 961 too, since 0 × 961 = 0
• 961: indeed, 961 is a multiple of itself, since 961 is evenly divisible by 961 (we have 961 / 961 = 1, so the remainder of this division is indeed zero)
• 1 922: indeed, 1 922 = 961 × 2
• 2 883: indeed, 2 883 = 961 × 3
• 3 844: indeed, 3 844 = 961 × 4
• 4 805: indeed, 4 805 = 961 × 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 961). 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 31). 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 961

• Preceding numbers: …959, 960
• Following numbers: 962, 963

## Nearest numbers from 961

• Preceding prime number: 953
• Following prime number: 967
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