Is 732 a prime number?

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

For 732, the answer is: No, 732 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 732) is as follows: 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732.

For 732 to be a prime number, it would have been required that 732 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

732 is a multiple of 1
732 is a multiple of 2
732 is a multiple of 3
732 is a multiple of 4
732 is a multiple of 6
732 is a multiple of 12
732 is a multiple of 61
732 is a multiple of 122
732 is a multiple of 183
732 is a multiple of 244
732 is a multiple of 366

For 732 to be a prime number, it would have been required that 732 has only two divisors, i.e., itself and 1.

Is 732 a deficient number?

No, 732 is not a deficient number: to be deficient, 732 should have been such that 732 is larger than the sum of its proper divisors, i.e., the divisors of 732 without 732 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 61 + 122 + 183 + 244 + 366 = 1 004).

In fact, 732 is an abundant number; 732 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 61 + 122 + 183 + 244 + 366 = 1 004). The smallest abundant number is 12.

Parity of 732

732 is an even number, because it is evenly divisible by 2: 732 / 2 = 366.

Find out more:

What is an even number?

Is 732 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 732 is about 27.055.

Thus, the square root of 732 is not an integer, and therefore 732 is not a square number.

What is the square number of 732?

The square of a number (here 732) is the result of the product of this number (732) by itself (i.e., 732 × 732); the square of 732 is sometimes called "raising 732 to the power 2", or "732 squared".

The square of 732 is 535 824 because 732 × 732 = 732² = 535 824.

As a consequence, 732 is the square root of 535 824.

Number of digits of 732

732 is a number with 3 digits.

What are the multiples of 732?

The multiples of 732 are all integers evenly divisible by 732, that is all numbers such that the remainder of the division by 732 is zero. There are infinitely many multiples of 732. The smallest multiples of 732 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 732 too, since 0 × 732 = 0
732: indeed, 732 is a multiple of itself, since 732 is evenly divisible by 732 (we have 732 / 732 = 1, so the remainder of this division is indeed zero)
1 464: indeed, 1 464 = 732 × 2
2 196: indeed, 2 196 = 732 × 3
2 928: indeed, 2 928 = 732 × 4
3 660: indeed, 3 660 = 732 × 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 732). 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 27.055). 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 732

Preceding numbers: …730, 731
Following numbers: 733, 734…

Nearest numbers from 732

Preceding prime number: 727
Following prime number: 733