Is 960 a prime number? What are the divisors of 960?

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.

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

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

To be 960 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.

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
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