Is 707 a prime number? What are the divisors of 707?

Is 707 a prime number?

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

For 707, the answer is: No, 707 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 707) is as follows: 1, 7, 101, 707.

To be 707 a prime number, it would have been required that 707 has only two divisors, i.e., itself and 1.

As a consequence:

  • 707 is a multiple of 1
  • 707 is a multiple of 7
  • 707 is a multiple of 101

To be 707 a prime number, it would have been required that 707 has only two divisors, i.e., itself and 1.

However, 707 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 707 = 7 x 101, where 7 and 101 are both prime numbers.

Is 707 a deficient number?

Yes, 707 is a deficient number, that is to say 707 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 707 without 707 itself (that is 1 + 7 + 101 = 109).

Parity of 707

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

Is 707 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 707 is about 26.589.

Thus, the square root of 707 is not an integer, and therefore 707 is not a square number.

What is the square number of 707?

The square of a number (here 707) is the result of the product of this number (707) by itself (i.e., 707 × 707); the square of 707 is sometimes called "raising 707 to the power 2", or "707 squared".

The square of 707 is 499 849 because 707 × 707 = 7072 = 499 849.

As a consequence, 707 is the square root of 499 849.

Number of digits of 707

707 is a number with 3 digits.

What are the multiples of 707?

The multiples of 707 are all integers evenly divisible by 707, that is all numbers such that the remainder of the division by 707 is zero. There are infinitely many multiples of 707. The smallest multiples of 707 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 707 too, since 0 × 707 = 0
  • 707: indeed, 707 is a multiple of itself, since 707 is evenly divisible by 707 (we have 707 / 707 = 1, so the remainder of this division is indeed zero)
  • 1 414: indeed, 1 414 = 707 × 2
  • 2 121: indeed, 2 121 = 707 × 3
  • 2 828: indeed, 2 828 = 707 × 4
  • 3 535: indeed, 3 535 = 707 × 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 707). 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 26.589). 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 707

  • Preceding numbers: …705, 706
  • Following numbers: 708, 709

Nearest numbers from 707

  • Preceding prime number: 701
  • Following prime number: 709
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