Is 973 a prime number?

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

For 973, the answer is: No, 973 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 973) is as follows: 1, 7, 139, 973.

For 973 to be a prime number, it would have been required that 973 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

973 is a multiple of 1
973 is a multiple of 7
973 is a multiple of 139

For 973 to be a prime number, it would have been required that 973 has only two divisors, i.e., itself and 1.

However, 973 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 973 = 7 x 139, where 7 and 139 are both prime numbers.

Is 973 a deficient number?

Yes, 973 is a deficient number, that is to say 973 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 973 without 973 itself (that is 1 + 7 + 139 = 147).

Parity of 973

973 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 973 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 973 is about 31.193.

Thus, the square root of 973 is not an integer, and therefore 973 is not a square number.

What is the square number of 973?

The square of a number (here 973) is the result of the product of this number (973) by itself (i.e., 973 × 973); the square of 973 is sometimes called "raising 973 to the power 2", or "973 squared".

The square of 973 is 946 729 because 973 × 973 = 973² = 946 729.

As a consequence, 973 is the square root of 946 729.

Number of digits of 973

973 is a number with 3 digits.

What are the multiples of 973?

The multiples of 973 are all integers evenly divisible by 973, that is all numbers such that the remainder of the division by 973 is zero. There are infinitely many multiples of 973. The smallest multiples of 973 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 973 too, since 0 × 973 = 0
973: indeed, 973 is a multiple of itself, since 973 is evenly divisible by 973 (we have 973 / 973 = 1, so the remainder of this division is indeed zero)
1 946: indeed, 1 946 = 973 × 2
2 919: indeed, 2 919 = 973 × 3
3 892: indeed, 3 892 = 973 × 4
4 865: indeed, 4 865 = 973 × 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 973). 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 31.193). 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 973

Preceding numbers: …971, 972
Following numbers: 974, 975…

Nearest numbers from 973

Preceding prime number: 971
Following prime number: 977