Is 825 a prime number?

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

For 825, the answer is: No, 825 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 825) is as follows: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825.

For 825 to be a prime number, it would have been required that 825 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 825 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 825 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

825 is a multiple of 1
825 is a multiple of 3
825 is a multiple of 5
825 is a multiple of 11
825 is a multiple of 15
825 is a multiple of 25
825 is a multiple of 33
825 is a multiple of 55
825 is a multiple of 75
825 is a multiple of 165
825 is a multiple of 275

For 825 to be a prime number, it would have been required that 825 has only two divisors, i.e., itself and 1.

Is 825 a deficient number?

Yes, 825 is a deficient number, that is to say 825 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 825 without 825 itself (that is 1 + 3 + 5 + 11 + 15 + 25 + 33 + 55 + 75 + 165 + 275 = 663).

Parity of 825

825 is an odd number, because it is not evenly divisible by 2.

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What is an even number?

Is 825 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 825 is about 28.723.

Thus, the square root of 825 is not an integer, and therefore 825 is not a square number.

What is the square number of 825?

The square of a number (here 825) is the result of the product of this number (825) by itself (i.e., 825 × 825); the square of 825 is sometimes called "raising 825 to the power 2", or "825 squared".

The square of 825 is 680 625 because 825 × 825 = 825² = 680 625.

As a consequence, 825 is the square root of 680 625.

Number of digits of 825

825 is a number with 3 digits.

What are the multiples of 825?

The multiples of 825 are all integers evenly divisible by 825, that is all numbers such that the remainder of the division by 825 is zero. There are infinitely many multiples of 825. The smallest multiples of 825 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 825 too, since 0 × 825 = 0
825: indeed, 825 is a multiple of itself, since 825 is evenly divisible by 825 (we have 825 / 825 = 1, so the remainder of this division is indeed zero)
1 650: indeed, 1 650 = 825 × 2
2 475: indeed, 2 475 = 825 × 3
3 300: indeed, 3 300 = 825 × 4
4 125: indeed, 4 125 = 825 × 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 825). 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 28.723). 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 825

Preceding numbers: …823, 824
Following numbers: 826, 827…

Nearest numbers from 825

Preceding prime number: 823
Following prime number: 827