Is 736 a prime number?

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

For 736, the answer is: No, 736 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 736) is as follows: 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.

For 736 to be a prime number, it would have been required that 736 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

736 is a multiple of 1
736 is a multiple of 2
736 is a multiple of 4
736 is a multiple of 8
736 is a multiple of 16
736 is a multiple of 23
736 is a multiple of 32
736 is a multiple of 46
736 is a multiple of 92
736 is a multiple of 184
736 is a multiple of 368

For 736 to be a prime number, it would have been required that 736 has only two divisors, i.e., itself and 1.

Is 736 a deficient number?

No, 736 is not a deficient number: to be deficient, 736 should have been such that 736 is larger than the sum of its proper divisors, i.e., the divisors of 736 without 736 itself (that is 1 + 2 + 4 + 8 + 16 + 23 + 32 + 46 + 92 + 184 + 368 = 776).

In fact, 736 is an abundant number; 736 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 16 + 23 + 32 + 46 + 92 + 184 + 368 = 776). The smallest abundant number is 12.

Parity of 736

736 is an even number, because it is evenly divisible by 2: 736 / 2 = 368.

Find out more:

What is an even number?

Is 736 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 736 is about 27.129.

Thus, the square root of 736 is not an integer, and therefore 736 is not a square number.

What is the square number of 736?

The square of a number (here 736) is the result of the product of this number (736) by itself (i.e., 736 × 736); the square of 736 is sometimes called "raising 736 to the power 2", or "736 squared".

The square of 736 is 541 696 because 736 × 736 = 736² = 541 696.

As a consequence, 736 is the square root of 541 696.

Number of digits of 736

736 is a number with 3 digits.

What are the multiples of 736?

The multiples of 736 are all integers evenly divisible by 736, that is all numbers such that the remainder of the division by 736 is zero. There are infinitely many multiples of 736. The smallest multiples of 736 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 736 too, since 0 × 736 = 0
736: indeed, 736 is a multiple of itself, since 736 is evenly divisible by 736 (we have 736 / 736 = 1, so the remainder of this division is indeed zero)
1 472: indeed, 1 472 = 736 × 2
2 208: indeed, 2 208 = 736 × 3
2 944: indeed, 2 944 = 736 × 4
3 680: indeed, 3 680 = 736 × 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 736). 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 27.129). 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 736

Preceding numbers: …734, 735
Following numbers: 737, 738…

Nearest numbers from 736

Preceding prime number: 733
Following prime number: 739