Is 738 a prime number?

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

For 738, the answer is: No, 738 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 738) is as follows: 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.

For 738 to be a prime number, it would have been required that 738 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

738 is a multiple of 1
738 is a multiple of 2
738 is a multiple of 3
738 is a multiple of 6
738 is a multiple of 9
738 is a multiple of 18
738 is a multiple of 41
738 is a multiple of 82
738 is a multiple of 123
738 is a multiple of 246
738 is a multiple of 369

For 738 to be a prime number, it would have been required that 738 has only two divisors, i.e., itself and 1.

Is 738 a deficient number?

No, 738 is not a deficient number: to be deficient, 738 should have been such that 738 is larger than the sum of its proper divisors, i.e., the divisors of 738 without 738 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 41 + 82 + 123 + 246 + 369 = 900).

In fact, 738 is an abundant number; 738 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 41 + 82 + 123 + 246 + 369 = 900). The smallest abundant number is 12.

Parity of 738

738 is an even number, because it is evenly divisible by 2: 738 / 2 = 369.

Find out more:

What is an even number?

Is 738 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 738 is about 27.166.

Thus, the square root of 738 is not an integer, and therefore 738 is not a square number.

What is the square number of 738?

The square of a number (here 738) is the result of the product of this number (738) by itself (i.e., 738 × 738); the square of 738 is sometimes called "raising 738 to the power 2", or "738 squared".

The square of 738 is 544 644 because 738 × 738 = 738² = 544 644.

As a consequence, 738 is the square root of 544 644.

Number of digits of 738

738 is a number with 3 digits.

What are the multiples of 738?

The multiples of 738 are all integers evenly divisible by 738, that is all numbers such that the remainder of the division by 738 is zero. There are infinitely many multiples of 738. The smallest multiples of 738 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 738 too, since 0 × 738 = 0
738: indeed, 738 is a multiple of itself, since 738 is evenly divisible by 738 (we have 738 / 738 = 1, so the remainder of this division is indeed zero)
1 476: indeed, 1 476 = 738 × 2
2 214: indeed, 2 214 = 738 × 3
2 952: indeed, 2 952 = 738 × 4
3 690: indeed, 3 690 = 738 × 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 738). 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 27.166). 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 738

Preceding numbers: …736, 737
Following numbers: 739, 740…

Nearest numbers from 738

Preceding prime number: 733
Following prime number: 739