Is 749 a prime number? What are the divisors of 749?

Is 749 a prime number?

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

For 749, the answer is: No, 749 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 749) is as follows: 1, 7, 107, 749.

To be 749 a prime number, it would have been required that 749 has only two divisors, i.e., itself and 1.

As a consequence:

  • 749 is a multiple of 1
  • 749 is a multiple of 7
  • 749 is a multiple of 107

To be 749 a prime number, it would have been required that 749 has only two divisors, i.e., itself and 1.

However, 749 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 749 = 7 x 107, where 7 and 107 are both prime numbers.

Is 749 a deficient number?

Yes, 749 is a deficient number, that is to say 749 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 749 without 749 itself (that is 1 + 7 + 107 = 115).

Parity of 749

749 is an odd number, because it is not evenly divisible by 2.

Is 749 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 749 is about 27.368.

Thus, the square root of 749 is not an integer, and therefore 749 is not a square number.

What is the square number of 749?

The square of a number (here 749) is the result of the product of this number (749) by itself (i.e., 749 × 749); the square of 749 is sometimes called "raising 749 to the power 2", or "749 squared".

The square of 749 is 561 001 because 749 × 749 = 7492 = 561 001.

As a consequence, 749 is the square root of 561 001.

Number of digits of 749

749 is a number with 3 digits.

What are the multiples of 749?

The multiples of 749 are all integers evenly divisible by 749, that is all numbers such that the remainder of the division by 749 is zero. There are infinitely many multiples of 749. The smallest multiples of 749 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 749 too, since 0 × 749 = 0
  • 749: indeed, 749 is a multiple of itself, since 749 is evenly divisible by 749 (we have 749 / 749 = 1, so the remainder of this division is indeed zero)
  • 1 498: indeed, 1 498 = 749 × 2
  • 2 247: indeed, 2 247 = 749 × 3
  • 2 996: indeed, 2 996 = 749 × 4
  • 3 745: indeed, 3 745 = 749 × 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 749). 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 27.368). 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 749

  • Preceding numbers: …747, 748
  • Following numbers: 750, 751

Nearest numbers from 749

  • Preceding prime number: 743
  • Following prime number: 751
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