Is 978 a prime number?

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

For 978, the answer is: No, 978 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 978) is as follows: 1, 2, 3, 6, 163, 326, 489, 978.

For 978 to be a prime number, it would have been required that 978 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

978 is a multiple of 1
978 is a multiple of 2
978 is a multiple of 3
978 is a multiple of 6
978 is a multiple of 163
978 is a multiple of 326
978 is a multiple of 489

For 978 to be a prime number, it would have been required that 978 has only two divisors, i.e., itself and 1.

Is 978 a deficient number?

No, 978 is not a deficient number: to be deficient, 978 should have been such that 978 is larger than the sum of its proper divisors, i.e., the divisors of 978 without 978 itself (that is 1 + 2 + 3 + 6 + 163 + 326 + 489 = 990).

In fact, 978 is an abundant number; 978 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 163 + 326 + 489 = 990). The smallest abundant number is 12.

Parity of 978

978 is an even number, because it is evenly divisible by 2: 978 / 2 = 489.

Find out more:

What is an even number?

Is 978 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 978 is about 31.273.

Thus, the square root of 978 is not an integer, and therefore 978 is not a square number.

What is the square number of 978?

The square of a number (here 978) is the result of the product of this number (978) by itself (i.e., 978 × 978); the square of 978 is sometimes called "raising 978 to the power 2", or "978 squared".

The square of 978 is 956 484 because 978 × 978 = 978² = 956 484.

As a consequence, 978 is the square root of 956 484.

Number of digits of 978

978 is a number with 3 digits.

What are the multiples of 978?

The multiples of 978 are all integers evenly divisible by 978, that is all numbers such that the remainder of the division by 978 is zero. There are infinitely many multiples of 978. The smallest multiples of 978 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 978 too, since 0 × 978 = 0
978: indeed, 978 is a multiple of itself, since 978 is evenly divisible by 978 (we have 978 / 978 = 1, so the remainder of this division is indeed zero)
1 956: indeed, 1 956 = 978 × 2
2 934: indeed, 2 934 = 978 × 3
3 912: indeed, 3 912 = 978 × 4
4 890: indeed, 4 890 = 978 × 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 978). 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 31.273). 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 978

Preceding numbers: …976, 977
Following numbers: 979, 980…

Nearest numbers from 978

Preceding prime number: 977
Following prime number: 983