Is 966 a prime number?

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

For 966, the answer is: No, 966 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 966) is as follows: 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966.

For 966 to be a prime number, it would have been required that 966 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

966 is a multiple of 1
966 is a multiple of 2
966 is a multiple of 3
966 is a multiple of 6
966 is a multiple of 7
966 is a multiple of 14
966 is a multiple of 21
966 is a multiple of 23
966 is a multiple of 42
966 is a multiple of 46
966 is a multiple of 69
966 is a multiple of 138
966 is a multiple of 161
966 is a multiple of 322
966 is a multiple of 483

For 966 to be a prime number, it would have been required that 966 has only two divisors, i.e., itself and 1.

Is 966 a deficient number?

No, 966 is not a deficient number: to be deficient, 966 should have been such that 966 is larger than the sum of its proper divisors, i.e., the divisors of 966 without 966 itself (that is 1 + 2 + 3 + 6 + 7 + 14 + 21 + 23 + 42 + 46 + 69 + 138 + 161 + 322 + 483 = 1 338).

In fact, 966 is an abundant number; 966 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 7 + 14 + 21 + 23 + 42 + 46 + 69 + 138 + 161 + 322 + 483 = 1 338). The smallest abundant number is 12.

Parity of 966

966 is an even number, because it is evenly divisible by 2: 966 / 2 = 483.

Find out more:

What is an even number?

Is 966 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 966 is about 31.081.

Thus, the square root of 966 is not an integer, and therefore 966 is not a square number.

What is the square number of 966?

The square of a number (here 966) is the result of the product of this number (966) by itself (i.e., 966 × 966); the square of 966 is sometimes called "raising 966 to the power 2", or "966 squared".

The square of 966 is 933 156 because 966 × 966 = 966² = 933 156.

As a consequence, 966 is the square root of 933 156.

Number of digits of 966

966 is a number with 3 digits.

What are the multiples of 966?

The multiples of 966 are all integers evenly divisible by 966, that is all numbers such that the remainder of the division by 966 is zero. There are infinitely many multiples of 966. The smallest multiples of 966 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 966 too, since 0 × 966 = 0
966: indeed, 966 is a multiple of itself, since 966 is evenly divisible by 966 (we have 966 / 966 = 1, so the remainder of this division is indeed zero)
1 932: indeed, 1 932 = 966 × 2
2 898: indeed, 2 898 = 966 × 3
3 864: indeed, 3 864 = 966 × 4
4 830: indeed, 4 830 = 966 × 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 966). 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 31.081). 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 966

Preceding numbers: …964, 965
Following numbers: 967, 968…

Nearest numbers from 966

Preceding prime number: 953
Following prime number: 967