Is 752 a prime number?

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

For 752, the answer is: No, 752 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 752) is as follows: 1, 2, 4, 8, 16, 47, 94, 188, 376, 752.

For 752 to be a prime number, it would have been required that 752 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

752 is a multiple of 1
752 is a multiple of 2
752 is a multiple of 4
752 is a multiple of 8
752 is a multiple of 16
752 is a multiple of 47
752 is a multiple of 94
752 is a multiple of 188
752 is a multiple of 376

For 752 to be a prime number, it would have been required that 752 has only two divisors, i.e., itself and 1.

Is 752 a deficient number?

Yes, 752 is a deficient number, that is to say 752 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 752 without 752 itself (that is 1 + 2 + 4 + 8 + 16 + 47 + 94 + 188 + 376 = 736).

Parity of 752

752 is an even number, because it is evenly divisible by 2: 752 / 2 = 376.

Find out more:

What is an even number?

Is 752 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 752 is about 27.423.

Thus, the square root of 752 is not an integer, and therefore 752 is not a square number.

What is the square number of 752?

The square of a number (here 752) is the result of the product of this number (752) by itself (i.e., 752 × 752); the square of 752 is sometimes called "raising 752 to the power 2", or "752 squared".

The square of 752 is 565 504 because 752 × 752 = 752² = 565 504.

As a consequence, 752 is the square root of 565 504.

Number of digits of 752

752 is a number with 3 digits.

What are the multiples of 752?

The multiples of 752 are all integers evenly divisible by 752, that is all numbers such that the remainder of the division by 752 is zero. There are infinitely many multiples of 752. The smallest multiples of 752 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 752 too, since 0 × 752 = 0
752: indeed, 752 is a multiple of itself, since 752 is evenly divisible by 752 (we have 752 / 752 = 1, so the remainder of this division is indeed zero)
1 504: indeed, 1 504 = 752 × 2
2 256: indeed, 2 256 = 752 × 3
3 008: indeed, 3 008 = 752 × 4
3 760: indeed, 3 760 = 752 × 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 752). 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 27.423). 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 752

Preceding numbers: …750, 751
Following numbers: 753, 754…

Nearest numbers from 752

Preceding prime number: 751
Following prime number: 757