Is 117 a prime number? What are the divisors of 117?

Is 117 a prime number?

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

For 117, the answer is: No, 117 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 117) is as follows: 1, 3, 9, 13, 39, 117.

To be 117 a prime number, it would have been required that 117 has only two divisors, i.e., itself and 1.

As a consequence:

  • 117 is a multiple of 1
  • 117 is a multiple of 3
  • 117 is a multiple of 9
  • 117 is a multiple of 13
  • 117 is a multiple of 39

To be 117 a prime number, it would have been required that 117 has only two divisors, i.e., itself and 1.

Is 117 a deficient number?

Yes, 117 is a deficient number, that is to say 117 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 117 without 117 itself (that is 1 + 3 + 9 + 13 + 39 = 65).

Parity of 117

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

Is 117 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 117 is about 10.817.

Thus, the square root of 117 is not an integer, and therefore 117 is not a square number.

What is the square number of 117?

The square of a number (here 117) is the result of the product of this number (117) by itself (i.e., 117 × 117); the square of 117 is sometimes called "raising 117 to the power 2", or "117 squared".

The square of 117 is 13 689 because 117 × 117 = 1172 = 13 689.

As a consequence, 117 is the square root of 13 689.

Number of digits of 117

117 is a number with 3 digits.

What are the multiples of 117?

The multiples of 117 are all integers evenly divisible by 117, that is all numbers such that the remainder of the division by 117 is zero. There are infinitely many multiples of 117. The smallest multiples of 117 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 117 too, since 0 × 117 = 0
  • 117: indeed, 117 is a multiple of itself, since 117 is evenly divisible by 117 (we have 117 / 117 = 1, so the remainder of this division is indeed zero)
  • 234: indeed, 234 = 117 × 2
  • 351: indeed, 351 = 117 × 3
  • 468: indeed, 468 = 117 × 4
  • 585: indeed, 585 = 117 × 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 117). 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 10.817). 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 117

  • Preceding numbers: …115, 116
  • Following numbers: 118, 119

Nearest numbers from 117

  • Preceding prime number: 113
  • Following prime number: 127
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