Is 252 a prime number?

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

For 252, the answer is: No, 252 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 252) is as follows: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.

For 252 to be a prime number, it would have been required that 252 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

252 is a multiple of 1
252 is a multiple of 2
252 is a multiple of 3
252 is a multiple of 4
252 is a multiple of 6
252 is a multiple of 7
252 is a multiple of 9
252 is a multiple of 12
252 is a multiple of 14
252 is a multiple of 18
252 is a multiple of 21
252 is a multiple of 28
252 is a multiple of 36
252 is a multiple of 42
252 is a multiple of 63
252 is a multiple of 84
252 is a multiple of 126

For 252 to be a prime number, it would have been required that 252 has only two divisors, i.e., itself and 1.

Is 252 a deficient number?

No, 252 is not a deficient number: to be deficient, 252 should have been such that 252 is larger than the sum of its proper divisors, i.e., the divisors of 252 without 252 itself (that is 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 63 + 84 + 126 = 476).

In fact, 252 is an abundant number; 252 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 63 + 84 + 126 = 476). The smallest abundant number is 12.

Parity of 252

252 is an even number, because it is evenly divisible by 2: 252 / 2 = 126.

Find out more:

What is an even number?

Is 252 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 252 is about 15.875.

Thus, the square root of 252 is not an integer, and therefore 252 is not a square number.

What is the square number of 252?

The square of a number (here 252) is the result of the product of this number (252) by itself (i.e., 252 × 252); the square of 252 is sometimes called "raising 252 to the power 2", or "252 squared".

The square of 252 is 63 504 because 252 × 252 = 252² = 63 504.

As a consequence, 252 is the square root of 63 504.

Number of digits of 252

252 is a number with 3 digits.

What are the multiples of 252?

The multiples of 252 are all integers evenly divisible by 252, that is all numbers such that the remainder of the division by 252 is zero. There are infinitely many multiples of 252. The smallest multiples of 252 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 252 too, since 0 × 252 = 0
252: indeed, 252 is a multiple of itself, since 252 is evenly divisible by 252 (we have 252 / 252 = 1, so the remainder of this division is indeed zero)
504: indeed, 504 = 252 × 2
756: indeed, 756 = 252 × 3
1 008: indeed, 1 008 = 252 × 4
1 260: indeed, 1 260 = 252 × 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 252). 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 15.875). 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 252

Preceding numbers: …250, 251
Following numbers: 253, 254…

Nearest numbers from 252

Preceding prime number: 251
Following prime number: 257