Is 708 a prime number? What are the divisors of 708?

Is 708 a prime number?

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

For 708, the answer is: No, 708 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 708) is as follows: 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708.

To be 708 a prime number, it would have been required that 708 has only two divisors, i.e., itself and 1.

As a consequence:

  • 708 is a multiple of 1
  • 708 is a multiple of 2
  • 708 is a multiple of 3
  • 708 is a multiple of 4
  • 708 is a multiple of 6
  • 708 is a multiple of 12
  • 708 is a multiple of 59
  • 708 is a multiple of 118
  • 708 is a multiple of 177
  • 708 is a multiple of 236
  • 708 is a multiple of 354

To be 708 a prime number, it would have been required that 708 has only two divisors, i.e., itself and 1.

Is 708 a deficient number?

No, 708 is not a deficient number: to be deficient, 708 should have been such that 708 is larger than the sum of its proper divisors, i.e., the divisors of 708 without 708 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 59 + 118 + 177 + 236 + 354 = 972).

In fact, 708 is an abundant number; 708 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 59 + 118 + 177 + 236 + 354 = 972). The smallest abundant number is 12.

Parity of 708

708 is an even number, because it is evenly divisible by 2: 708 / 2 = 354.

Is 708 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 708 is about 26.608.

Thus, the square root of 708 is not an integer, and therefore 708 is not a square number.

What is the square number of 708?

The square of a number (here 708) is the result of the product of this number (708) by itself (i.e., 708 × 708); the square of 708 is sometimes called "raising 708 to the power 2", or "708 squared".

The square of 708 is 501 264 because 708 × 708 = 7082 = 501 264.

As a consequence, 708 is the square root of 501 264.

Number of digits of 708

708 is a number with 3 digits.

What are the multiples of 708?

The multiples of 708 are all integers evenly divisible by 708, that is all numbers such that the remainder of the division by 708 is zero. There are infinitely many multiples of 708. The smallest multiples of 708 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 708 too, since 0 × 708 = 0
  • 708: indeed, 708 is a multiple of itself, since 708 is evenly divisible by 708 (we have 708 / 708 = 1, so the remainder of this division is indeed zero)
  • 1 416: indeed, 1 416 = 708 × 2
  • 2 124: indeed, 2 124 = 708 × 3
  • 2 832: indeed, 2 832 = 708 × 4
  • 3 540: indeed, 3 540 = 708 × 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 708). 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 26.608). 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 708

  • Preceding numbers: …706, 707
  • Following numbers: 709, 710

Nearest numbers from 708

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