Is 960 a prime number?

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

For 960, the answer is: No, 960 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 960) is as follows: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960.

For 960 to be a prime number, it would have been required that 960 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 960 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 960 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

960 is a multiple of 1
960 is a multiple of 2
960 is a multiple of 3
960 is a multiple of 4
960 is a multiple of 5
960 is a multiple of 6
960 is a multiple of 8
960 is a multiple of 10
960 is a multiple of 12
960 is a multiple of 15
960 is a multiple of 16
960 is a multiple of 20
960 is a multiple of 24
960 is a multiple of 30
960 is a multiple of 32
960 is a multiple of 40
960 is a multiple of 48
960 is a multiple of 60
960 is a multiple of 64
960 is a multiple of 80
960 is a multiple of 96
960 is a multiple of 120
960 is a multiple of 160
960 is a multiple of 192
960 is a multiple of 240
960 is a multiple of 320
960 is a multiple of 480

For 960 to be a prime number, it would have been required that 960 has only two divisors, i.e., itself and 1.

Is 960 a deficient number?

No, 960 is not a deficient number: to be deficient, 960 should have been such that 960 is larger than the sum of its proper divisors, i.e., the divisors of 960 without 960 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 160 + 192 + 240 + 320 + 480 = 2 088).

In fact, 960 is an abundant number; 960 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 64 + 80 + 96 + 120 + 160 + 192 + 240 + 320 + 480 = 2 088). The smallest abundant number is 12.

Parity of 960

960 is an even number, because it is evenly divisible by 2: 960 / 2 = 480.

Find out more:

What is an even number?

Is 960 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 960 is about 30.984.

Thus, the square root of 960 is not an integer, and therefore 960 is not a square number.

What is the square number of 960?

The square of a number (here 960) is the result of the product of this number (960) by itself (i.e., 960 × 960); the square of 960 is sometimes called "raising 960 to the power 2", or "960 squared".

The square of 960 is 921 600 because 960 × 960 = 960² = 921 600.

As a consequence, 960 is the square root of 921 600.

Number of digits of 960

960 is a number with 3 digits.

What are the multiples of 960?

The multiples of 960 are all integers evenly divisible by 960, that is all numbers such that the remainder of the division by 960 is zero. There are infinitely many multiples of 960. The smallest multiples of 960 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 960 too, since 0 × 960 = 0
960: indeed, 960 is a multiple of itself, since 960 is evenly divisible by 960 (we have 960 / 960 = 1, so the remainder of this division is indeed zero)
1 920: indeed, 1 920 = 960 × 2
2 880: indeed, 2 880 = 960 × 3
3 840: indeed, 3 840 = 960 × 4
4 800: indeed, 4 800 = 960 × 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 960). 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 30.984). 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 960

Preceding numbers: …958, 959
Following numbers: 961, 962…

Nearest numbers from 960

Preceding prime number: 953
Following prime number: 967