Is 980 a prime number?

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

For 980, the answer is: No, 980 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 980) is as follows: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.

For 980 to be a prime number, it would have been required that 980 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 980 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 980 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

980 is a multiple of 1
980 is a multiple of 2
980 is a multiple of 4
980 is a multiple of 5
980 is a multiple of 7
980 is a multiple of 10
980 is a multiple of 14
980 is a multiple of 20
980 is a multiple of 28
980 is a multiple of 35
980 is a multiple of 49
980 is a multiple of 70
980 is a multiple of 98
980 is a multiple of 140
980 is a multiple of 196
980 is a multiple of 245
980 is a multiple of 490

For 980 to be a prime number, it would have been required that 980 has only two divisors, i.e., itself and 1.

Is 980 a deficient number?

No, 980 is not a deficient number: to be deficient, 980 should have been such that 980 is larger than the sum of its proper divisors, i.e., the divisors of 980 without 980 itself (that is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 49 + 70 + 98 + 140 + 196 + 245 + 490 = 1 414).

In fact, 980 is an abundant number; 980 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 49 + 70 + 98 + 140 + 196 + 245 + 490 = 1 414). The smallest abundant number is 12.

Parity of 980

980 is an even number, because it is evenly divisible by 2: 980 / 2 = 490.

Find out more:

What is an even number?

Is 980 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 980 is about 31.305.

Thus, the square root of 980 is not an integer, and therefore 980 is not a square number.

What is the square number of 980?

The square of a number (here 980) is the result of the product of this number (980) by itself (i.e., 980 × 980); the square of 980 is sometimes called "raising 980 to the power 2", or "980 squared".

The square of 980 is 960 400 because 980 × 980 = 980² = 960 400.

As a consequence, 980 is the square root of 960 400.

Number of digits of 980

980 is a number with 3 digits.

What are the multiples of 980?

The multiples of 980 are all integers evenly divisible by 980, that is all numbers such that the remainder of the division by 980 is zero. There are infinitely many multiples of 980. The smallest multiples of 980 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 980 too, since 0 × 980 = 0
980: indeed, 980 is a multiple of itself, since 980 is evenly divisible by 980 (we have 980 / 980 = 1, so the remainder of this division is indeed zero)
1 960: indeed, 1 960 = 980 × 2
2 940: indeed, 2 940 = 980 × 3
3 920: indeed, 3 920 = 980 × 4
4 900: indeed, 4 900 = 980 × 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 980). 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 31.305). 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 980

Preceding numbers: …978, 979
Following numbers: 981, 982…

Nearest numbers from 980

Preceding prime number: 977
Following prime number: 983