Is 972 a prime number?

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

For 972, the answer is: No, 972 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 972) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.

For 972 to be a prime number, it would have been required that 972 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

972 is a multiple of 1
972 is a multiple of 2
972 is a multiple of 3
972 is a multiple of 4
972 is a multiple of 6
972 is a multiple of 9
972 is a multiple of 12
972 is a multiple of 18
972 is a multiple of 27
972 is a multiple of 36
972 is a multiple of 54
972 is a multiple of 81
972 is a multiple of 108
972 is a multiple of 162
972 is a multiple of 243
972 is a multiple of 324
972 is a multiple of 486

For 972 to be a prime number, it would have been required that 972 has only two divisors, i.e., itself and 1.

Is 972 a deficient number?

No, 972 is not a deficient number: to be deficient, 972 should have been such that 972 is larger than the sum of its proper divisors, i.e., the divisors of 972 without 972 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 = 1 576).

In fact, 972 is an abundant number; 972 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 = 1 576). The smallest abundant number is 12.

Parity of 972

972 is an even number, because it is evenly divisible by 2: 972 / 2 = 486.

Find out more:

What is an even number?

Is 972 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 972 is about 31.177.

Thus, the square root of 972 is not an integer, and therefore 972 is not a square number.

What is the square number of 972?

The square of a number (here 972) is the result of the product of this number (972) by itself (i.e., 972 × 972); the square of 972 is sometimes called "raising 972 to the power 2", or "972 squared".

The square of 972 is 944 784 because 972 × 972 = 972² = 944 784.

As a consequence, 972 is the square root of 944 784.

Number of digits of 972

972 is a number with 3 digits.

What are the multiples of 972?

The multiples of 972 are all integers evenly divisible by 972, that is all numbers such that the remainder of the division by 972 is zero. There are infinitely many multiples of 972. The smallest multiples of 972 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 972 too, since 0 × 972 = 0
972: indeed, 972 is a multiple of itself, since 972 is evenly divisible by 972 (we have 972 / 972 = 1, so the remainder of this division is indeed zero)
1 944: indeed, 1 944 = 972 × 2
2 916: indeed, 2 916 = 972 × 3
3 888: indeed, 3 888 = 972 × 4
4 860: indeed, 4 860 = 972 × 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 972). 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 31.177). 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 972

Preceding numbers: …970, 971
Following numbers: 973, 974…

Nearest numbers from 972

Preceding prime number: 971
Following prime number: 977