Is 974 a prime number?

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

For 974, the answer is: No, 974 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 974) is as follows: 1, 2, 487, 974.

For 974 to be a prime number, it would have been required that 974 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

974 is a multiple of 1
974 is a multiple of 2
974 is a multiple of 487

For 974 to be a prime number, it would have been required that 974 has only two divisors, i.e., itself and 1.

However, 974 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 974 = 2 x 487, where 2 and 487 are both prime numbers.

Is 974 a deficient number?

Yes, 974 is a deficient number, that is to say 974 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 974 without 974 itself (that is 1 + 2 + 487 = 490).

Parity of 974

974 is an even number, because it is evenly divisible by 2: 974 / 2 = 487.

Find out more:

What is an even number?

Is 974 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 974 is about 31.209.

Thus, the square root of 974 is not an integer, and therefore 974 is not a square number.

What is the square number of 974?

The square of a number (here 974) is the result of the product of this number (974) by itself (i.e., 974 × 974); the square of 974 is sometimes called "raising 974 to the power 2", or "974 squared".

The square of 974 is 948 676 because 974 × 974 = 974² = 948 676.

As a consequence, 974 is the square root of 948 676.

Number of digits of 974

974 is a number with 3 digits.

What are the multiples of 974?

The multiples of 974 are all integers evenly divisible by 974, that is all numbers such that the remainder of the division by 974 is zero. There are infinitely many multiples of 974. The smallest multiples of 974 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 974 too, since 0 × 974 = 0
974: indeed, 974 is a multiple of itself, since 974 is evenly divisible by 974 (we have 974 / 974 = 1, so the remainder of this division is indeed zero)
1 948: indeed, 1 948 = 974 × 2
2 922: indeed, 2 922 = 974 × 3
3 896: indeed, 3 896 = 974 × 4
4 870: indeed, 4 870 = 974 × 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 974). 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 31.209). 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 974

Preceding numbers: …972, 973
Following numbers: 975, 976…

Nearest numbers from 974

Preceding prime number: 971
Following prime number: 977