Is 968 a prime number?

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

For 968, the answer is: No, 968 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 968) is as follows: 1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968.

For 968 to be a prime number, it would have been required that 968 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

968 is a multiple of 1
968 is a multiple of 2
968 is a multiple of 4
968 is a multiple of 8
968 is a multiple of 11
968 is a multiple of 22
968 is a multiple of 44
968 is a multiple of 88
968 is a multiple of 121
968 is a multiple of 242
968 is a multiple of 484

For 968 to be a prime number, it would have been required that 968 has only two divisors, i.e., itself and 1.

Is 968 a deficient number?

No, 968 is not a deficient number: to be deficient, 968 should have been such that 968 is larger than the sum of its proper divisors, i.e., the divisors of 968 without 968 itself (that is 1 + 2 + 4 + 8 + 11 + 22 + 44 + 88 + 121 + 242 + 484 = 1 027).

In fact, 968 is an abundant number; 968 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 11 + 22 + 44 + 88 + 121 + 242 + 484 = 1 027). The smallest abundant number is 12.

Parity of 968

968 is an even number, because it is evenly divisible by 2: 968 / 2 = 484.

Find out more:

What is an even number?

Is 968 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 968 is about 31.113.

Thus, the square root of 968 is not an integer, and therefore 968 is not a square number.

What is the square number of 968?

The square of a number (here 968) is the result of the product of this number (968) by itself (i.e., 968 × 968); the square of 968 is sometimes called "raising 968 to the power 2", or "968 squared".

The square of 968 is 937 024 because 968 × 968 = 968² = 937 024.

As a consequence, 968 is the square root of 937 024.

Number of digits of 968

968 is a number with 3 digits.

What are the multiples of 968?

The multiples of 968 are all integers evenly divisible by 968, that is all numbers such that the remainder of the division by 968 is zero. There are infinitely many multiples of 968. The smallest multiples of 968 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 968 too, since 0 × 968 = 0
968: indeed, 968 is a multiple of itself, since 968 is evenly divisible by 968 (we have 968 / 968 = 1, so the remainder of this division is indeed zero)
1 936: indeed, 1 936 = 968 × 2
2 904: indeed, 2 904 = 968 × 3
3 872: indeed, 3 872 = 968 × 4
4 840: indeed, 4 840 = 968 × 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 968). 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 31.113). 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 968

Preceding numbers: …966, 967
Following numbers: 969, 970…

Nearest numbers from 968

Preceding prime number: 967
Following prime number: 971