Is 742 a prime number?

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

For 742, the answer is: No, 742 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 742) is as follows: 1, 2, 7, 14, 53, 106, 371, 742.

For 742 to be a prime number, it would have been required that 742 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

742 is a multiple of 1
742 is a multiple of 2
742 is a multiple of 7
742 is a multiple of 14
742 is a multiple of 53
742 is a multiple of 106
742 is a multiple of 371

For 742 to be a prime number, it would have been required that 742 has only two divisors, i.e., itself and 1.

Is 742 a deficient number?

Yes, 742 is a deficient number, that is to say 742 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 742 without 742 itself (that is 1 + 2 + 7 + 14 + 53 + 106 + 371 = 554).

Parity of 742

742 is an even number, because it is evenly divisible by 2: 742 / 2 = 371.

Find out more:

What is an even number?

Is 742 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 742 is about 27.240.

Thus, the square root of 742 is not an integer, and therefore 742 is not a square number.

What is the square number of 742?

The square of a number (here 742) is the result of the product of this number (742) by itself (i.e., 742 × 742); the square of 742 is sometimes called "raising 742 to the power 2", or "742 squared".

The square of 742 is 550 564 because 742 × 742 = 742² = 550 564.

As a consequence, 742 is the square root of 550 564.

Number of digits of 742

742 is a number with 3 digits.

What are the multiples of 742?

The multiples of 742 are all integers evenly divisible by 742, that is all numbers such that the remainder of the division by 742 is zero. There are infinitely many multiples of 742. The smallest multiples of 742 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 742 too, since 0 × 742 = 0
742: indeed, 742 is a multiple of itself, since 742 is evenly divisible by 742 (we have 742 / 742 = 1, so the remainder of this division is indeed zero)
1 484: indeed, 1 484 = 742 × 2
2 226: indeed, 2 226 = 742 × 3
2 968: indeed, 2 968 = 742 × 4
3 710: indeed, 3 710 = 742 × 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 742). 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 27.240). 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 742

Preceding numbers: …740, 741
Following numbers: 743, 744…

Nearest numbers from 742

Preceding prime number: 739
Following prime number: 743