Is 737 a prime number?

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

For 737, the answer is: No, 737 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 737) is as follows: 1, 11, 67, 737.

For 737 to be a prime number, it would have been required that 737 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

737 is a multiple of 1
737 is a multiple of 11
737 is a multiple of 67

For 737 to be a prime number, it would have been required that 737 has only two divisors, i.e., itself and 1.

However, 737 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 737 = 11 x 67, where 11 and 67 are both prime numbers.

Is 737 a deficient number?

Yes, 737 is a deficient number, that is to say 737 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 737 without 737 itself (that is 1 + 11 + 67 = 79).

Parity of 737

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

Find out more:

What is an even number?

Is 737 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 737 is about 27.148.

Thus, the square root of 737 is not an integer, and therefore 737 is not a square number.

What is the square number of 737?

The square of a number (here 737) is the result of the product of this number (737) by itself (i.e., 737 × 737); the square of 737 is sometimes called "raising 737 to the power 2", or "737 squared".

The square of 737 is 543 169 because 737 × 737 = 737² = 543 169.

As a consequence, 737 is the square root of 543 169.

Number of digits of 737

737 is a number with 3 digits.

What are the multiples of 737?

The multiples of 737 are all integers evenly divisible by 737, that is all numbers such that the remainder of the division by 737 is zero. There are infinitely many multiples of 737. The smallest multiples of 737 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 737 too, since 0 × 737 = 0
737: indeed, 737 is a multiple of itself, since 737 is evenly divisible by 737 (we have 737 / 737 = 1, so the remainder of this division is indeed zero)
1 474: indeed, 1 474 = 737 × 2
2 211: indeed, 2 211 = 737 × 3
2 948: indeed, 2 948 = 737 × 4
3 685: indeed, 3 685 = 737 × 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 737). 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 27.148). 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 737

Preceding numbers: …735, 736
Following numbers: 738, 739…

Nearest numbers from 737

Preceding prime number: 733
Following prime number: 739