Is 917 a prime number?

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

For 917, the answer is: No, 917 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 917) is as follows: 1, 7, 131, 917.

For 917 to be a prime number, it would have been required that 917 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

917 is a multiple of 1
917 is a multiple of 7
917 is a multiple of 131

For 917 to be a prime number, it would have been required that 917 has only two divisors, i.e., itself and 1.

However, 917 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 917 = 7 x 131, where 7 and 131 are both prime numbers.

Is 917 a deficient number?

Yes, 917 is a deficient number, that is to say 917 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 917 without 917 itself (that is 1 + 7 + 131 = 139).

Parity of 917

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

Find out more:

What is an even number?

Is 917 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 917 is about 30.282.

Thus, the square root of 917 is not an integer, and therefore 917 is not a square number.

What is the square number of 917?

The square of a number (here 917) is the result of the product of this number (917) by itself (i.e., 917 × 917); the square of 917 is sometimes called "raising 917 to the power 2", or "917 squared".

The square of 917 is 840 889 because 917 × 917 = 917² = 840 889.

As a consequence, 917 is the square root of 840 889.

Number of digits of 917

917 is a number with 3 digits.

What are the multiples of 917?

The multiples of 917 are all integers evenly divisible by 917, that is all numbers such that the remainder of the division by 917 is zero. There are infinitely many multiples of 917. The smallest multiples of 917 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 917 too, since 0 × 917 = 0
917: indeed, 917 is a multiple of itself, since 917 is evenly divisible by 917 (we have 917 / 917 = 1, so the remainder of this division is indeed zero)
1 834: indeed, 1 834 = 917 × 2
2 751: indeed, 2 751 = 917 × 3
3 668: indeed, 3 668 = 917 × 4
4 585: indeed, 4 585 = 917 × 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 917). 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 30.282). 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 917

Preceding numbers: …915, 916
Following numbers: 918, 919…

Nearest numbers from 917

Preceding prime number: 911
Following prime number: 919