Is 744 a prime number?

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

For 744, the answer is: No, 744 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 744) is as follows: 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744.

For 744 to be a prime number, it would have been required that 744 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

744 is a multiple of 1
744 is a multiple of 2
744 is a multiple of 3
744 is a multiple of 4
744 is a multiple of 6
744 is a multiple of 8
744 is a multiple of 12
744 is a multiple of 24
744 is a multiple of 31
744 is a multiple of 62
744 is a multiple of 93
744 is a multiple of 124
744 is a multiple of 186
744 is a multiple of 248
744 is a multiple of 372

For 744 to be a prime number, it would have been required that 744 has only two divisors, i.e., itself and 1.

Is 744 a deficient number?

No, 744 is not a deficient number: to be deficient, 744 should have been such that 744 is larger than the sum of its proper divisors, i.e., the divisors of 744 without 744 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 31 + 62 + 93 + 124 + 186 + 248 + 372 = 1 176).

In fact, 744 is an abundant number; 744 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 31 + 62 + 93 + 124 + 186 + 248 + 372 = 1 176). The smallest abundant number is 12.

Parity of 744

744 is an even number, because it is evenly divisible by 2: 744 / 2 = 372.

Find out more:

What is an even number?

Is 744 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 744 is about 27.276.

Thus, the square root of 744 is not an integer, and therefore 744 is not a square number.

What is the square number of 744?

The square of a number (here 744) is the result of the product of this number (744) by itself (i.e., 744 × 744); the square of 744 is sometimes called "raising 744 to the power 2", or "744 squared".

The square of 744 is 553 536 because 744 × 744 = 744² = 553 536.

As a consequence, 744 is the square root of 553 536.

Number of digits of 744

744 is a number with 3 digits.

What are the multiples of 744?

The multiples of 744 are all integers evenly divisible by 744, that is all numbers such that the remainder of the division by 744 is zero. There are infinitely many multiples of 744. The smallest multiples of 744 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 744 too, since 0 × 744 = 0
744: indeed, 744 is a multiple of itself, since 744 is evenly divisible by 744 (we have 744 / 744 = 1, so the remainder of this division is indeed zero)
1 488: indeed, 1 488 = 744 × 2
2 232: indeed, 2 232 = 744 × 3
2 976: indeed, 2 976 = 744 × 4
3 720: indeed, 3 720 = 744 × 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 744). 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 27.276). 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 744

Preceding numbers: …742, 743
Following numbers: 745, 746…

Nearest numbers from 744

Preceding prime number: 743
Following prime number: 751