Is 860 a prime number?

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

For 860, the answer is: No, 860 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 860) is as follows: 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860.

For 860 to be a prime number, it would have been required that 860 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 860 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 860 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

860 is a multiple of 1
860 is a multiple of 2
860 is a multiple of 4
860 is a multiple of 5
860 is a multiple of 10
860 is a multiple of 20
860 is a multiple of 43
860 is a multiple of 86
860 is a multiple of 172
860 is a multiple of 215
860 is a multiple of 430

For 860 to be a prime number, it would have been required that 860 has only two divisors, i.e., itself and 1.

Is 860 a deficient number?

No, 860 is not a deficient number: to be deficient, 860 should have been such that 860 is larger than the sum of its proper divisors, i.e., the divisors of 860 without 860 itself (that is 1 + 2 + 4 + 5 + 10 + 20 + 43 + 86 + 172 + 215 + 430 = 988).

In fact, 860 is an abundant number; 860 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 + 20 + 43 + 86 + 172 + 215 + 430 = 988). The smallest abundant number is 12.

Parity of 860

860 is an even number, because it is evenly divisible by 2: 860 / 2 = 430.

Find out more:

What is an even number?

Is 860 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 860 is about 29.326.

Thus, the square root of 860 is not an integer, and therefore 860 is not a square number.

What is the square number of 860?

The square of a number (here 860) is the result of the product of this number (860) by itself (i.e., 860 × 860); the square of 860 is sometimes called "raising 860 to the power 2", or "860 squared".

The square of 860 is 739 600 because 860 × 860 = 860² = 739 600.

As a consequence, 860 is the square root of 739 600.

Number of digits of 860

860 is a number with 3 digits.

What are the multiples of 860?

The multiples of 860 are all integers evenly divisible by 860, that is all numbers such that the remainder of the division by 860 is zero. There are infinitely many multiples of 860. The smallest multiples of 860 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 860 too, since 0 × 860 = 0
860: indeed, 860 is a multiple of itself, since 860 is evenly divisible by 860 (we have 860 / 860 = 1, so the remainder of this division is indeed zero)
1 720: indeed, 1 720 = 860 × 2
2 580: indeed, 2 580 = 860 × 3
3 440: indeed, 3 440 = 860 × 4
4 300: indeed, 4 300 = 860 × 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 860). 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 29.326). 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 860

Preceding numbers: …858, 859
Following numbers: 861, 862…

Nearest numbers from 860

Preceding prime number: 859
Following prime number: 863