Is 850 a prime number?

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

For 850, the answer is: No, 850 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 850) is as follows: 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850.

For 850 to be a prime number, it would have been required that 850 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 850 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 850 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

850 is a multiple of 1
850 is a multiple of 2
850 is a multiple of 5
850 is a multiple of 10
850 is a multiple of 17
850 is a multiple of 25
850 is a multiple of 34
850 is a multiple of 50
850 is a multiple of 85
850 is a multiple of 170
850 is a multiple of 425

For 850 to be a prime number, it would have been required that 850 has only two divisors, i.e., itself and 1.

Is 850 a deficient number?

Yes, 850 is a deficient number, that is to say 850 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 850 without 850 itself (that is 1 + 2 + 5 + 10 + 17 + 25 + 34 + 50 + 85 + 170 + 425 = 824).

Parity of 850

850 is an even number, because it is evenly divisible by 2: 850 / 2 = 425.

Find out more:

What is an even number?

Is 850 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 850 is about 29.155.

Thus, the square root of 850 is not an integer, and therefore 850 is not a square number.

What is the square number of 850?

The square of a number (here 850) is the result of the product of this number (850) by itself (i.e., 850 × 850); the square of 850 is sometimes called "raising 850 to the power 2", or "850 squared".

The square of 850 is 722 500 because 850 × 850 = 850² = 722 500.

As a consequence, 850 is the square root of 722 500.

Number of digits of 850

850 is a number with 3 digits.

What are the multiples of 850?

The multiples of 850 are all integers evenly divisible by 850, that is all numbers such that the remainder of the division by 850 is zero. There are infinitely many multiples of 850. The smallest multiples of 850 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 850 too, since 0 × 850 = 0
850: indeed, 850 is a multiple of itself, since 850 is evenly divisible by 850 (we have 850 / 850 = 1, so the remainder of this division is indeed zero)
1 700: indeed, 1 700 = 850 × 2
2 550: indeed, 2 550 = 850 × 3
3 400: indeed, 3 400 = 850 × 4
4 250: indeed, 4 250 = 850 × 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 850). 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 29.155). 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 850

Preceding numbers: …848, 849
Following numbers: 851, 852…

Nearest numbers from 850

Preceding prime number: 839
Following prime number: 853