Is 748 a prime number?

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

For 748, the answer is: No, 748 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 748) is as follows: 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748.

For 748 to be a prime number, it would have been required that 748 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

748 is a multiple of 1
748 is a multiple of 2
748 is a multiple of 4
748 is a multiple of 11
748 is a multiple of 17
748 is a multiple of 22
748 is a multiple of 34
748 is a multiple of 44
748 is a multiple of 68
748 is a multiple of 187
748 is a multiple of 374

For 748 to be a prime number, it would have been required that 748 has only two divisors, i.e., itself and 1.

Is 748 a deficient number?

No, 748 is not a deficient number: to be deficient, 748 should have been such that 748 is larger than the sum of its proper divisors, i.e., the divisors of 748 without 748 itself (that is 1 + 2 + 4 + 11 + 17 + 22 + 34 + 44 + 68 + 187 + 374 = 764).

In fact, 748 is an abundant number; 748 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 11 + 17 + 22 + 34 + 44 + 68 + 187 + 374 = 764). The smallest abundant number is 12.

Parity of 748

748 is an even number, because it is evenly divisible by 2: 748 / 2 = 374.

Find out more:

What is an even number?

Is 748 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 748 is about 27.350.

Thus, the square root of 748 is not an integer, and therefore 748 is not a square number.

What is the square number of 748?

The square of a number (here 748) is the result of the product of this number (748) by itself (i.e., 748 × 748); the square of 748 is sometimes called "raising 748 to the power 2", or "748 squared".

The square of 748 is 559 504 because 748 × 748 = 748² = 559 504.

As a consequence, 748 is the square root of 559 504.

Number of digits of 748

748 is a number with 3 digits.

What are the multiples of 748?

The multiples of 748 are all integers evenly divisible by 748, that is all numbers such that the remainder of the division by 748 is zero. There are infinitely many multiples of 748. The smallest multiples of 748 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 748 too, since 0 × 748 = 0
748: indeed, 748 is a multiple of itself, since 748 is evenly divisible by 748 (we have 748 / 748 = 1, so the remainder of this division is indeed zero)
1 496: indeed, 1 496 = 748 × 2
2 244: indeed, 2 244 = 748 × 3
2 992: indeed, 2 992 = 748 × 4
3 740: indeed, 3 740 = 748 × 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 748). 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 27.350). 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 748

Preceding numbers: …746, 747
Following numbers: 749, 750…

Nearest numbers from 748

Preceding prime number: 743
Following prime number: 751