Is 747 a prime number?

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

For 747, the answer is: No, 747 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 747) is as follows: 1, 3, 9, 83, 249, 747.

For 747 to be a prime number, it would have been required that 747 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

747 is a multiple of 1
747 is a multiple of 3
747 is a multiple of 9
747 is a multiple of 83
747 is a multiple of 249

For 747 to be a prime number, it would have been required that 747 has only two divisors, i.e., itself and 1.

Is 747 a deficient number?

Yes, 747 is a deficient number, that is to say 747 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 747 without 747 itself (that is 1 + 3 + 9 + 83 + 249 = 345).

Parity of 747

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

Find out more:

What is an even number?

Is 747 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 747 is about 27.331.

Thus, the square root of 747 is not an integer, and therefore 747 is not a square number.

What is the square number of 747?

The square of a number (here 747) is the result of the product of this number (747) by itself (i.e., 747 × 747); the square of 747 is sometimes called "raising 747 to the power 2", or "747 squared".

The square of 747 is 558 009 because 747 × 747 = 747² = 558 009.

As a consequence, 747 is the square root of 558 009.

Number of digits of 747

747 is a number with 3 digits.

What are the multiples of 747?

The multiples of 747 are all integers evenly divisible by 747, that is all numbers such that the remainder of the division by 747 is zero. There are infinitely many multiples of 747. The smallest multiples of 747 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 747 too, since 0 × 747 = 0
747: indeed, 747 is a multiple of itself, since 747 is evenly divisible by 747 (we have 747 / 747 = 1, so the remainder of this division is indeed zero)
1 494: indeed, 1 494 = 747 × 2
2 241: indeed, 2 241 = 747 × 3
2 988: indeed, 2 988 = 747 × 4
3 735: indeed, 3 735 = 747 × 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 747). 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 27.331). 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 747

Preceding numbers: …745, 746
Following numbers: 748, 749…

Nearest numbers from 747

Preceding prime number: 743
Following prime number: 751