Is 676 a prime number? What are the divisors of 676?

Is 676 a prime number?

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

For 676, the answer is: No, 676 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 676) is as follows: 1, 2, 4, 13, 26, 52, 169, 338, 676.

To be 676 a prime number, it would have been required that 676 has only two divisors, i.e., itself and 1.

As a consequence:

  • 676 is a multiple of 1
  • 676 is a multiple of 2
  • 676 is a multiple of 4
  • 676 is a multiple of 13
  • 676 is a multiple of 26
  • 676 is a multiple of 52
  • 676 is a multiple of 169
  • 676 is a multiple of 338

To be 676 a prime number, it would have been required that 676 has only two divisors, i.e., itself and 1.

Is 676 a deficient number?

Yes, 676 is a deficient number, that is to say 676 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 676 without 676 itself (that is 1 + 2 + 4 + 13 + 26 + 52 + 169 + 338 = 605).

Parity of 676

676 is an even number, because it is evenly divisible by 2: 676 / 2 = 338.

Is 676 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 676 is 26.

Therefore, the square root of 676 is an integer, and as a consequence 676 is a perfect square.

As a consequence, 26 is the square root of 676.

What is the square number of 676?

The square of a number (here 676) is the result of the product of this number (676) by itself (i.e., 676 × 676); the square of 676 is sometimes called "raising 676 to the power 2", or "676 squared".

The square of 676 is 456 976 because 676 × 676 = 6762 = 456 976.

As a consequence, 676 is the square root of 456 976.

Number of digits of 676

676 is a number with 3 digits.

What are the multiples of 676?

The multiples of 676 are all integers evenly divisible by 676, that is all numbers such that the remainder of the division by 676 is zero. There are infinitely many multiples of 676. The smallest multiples of 676 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 676 too, since 0 × 676 = 0
  • 676: indeed, 676 is a multiple of itself, since 676 is evenly divisible by 676 (we have 676 / 676 = 1, so the remainder of this division is indeed zero)
  • 1 352: indeed, 1 352 = 676 × 2
  • 2 028: indeed, 2 028 = 676 × 3
  • 2 704: indeed, 2 704 = 676 × 4
  • 3 380: indeed, 3 380 = 676 × 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 676). 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 26). 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 676

  • Preceding numbers: …674, 675
  • Following numbers: 677, 678

Nearest numbers from 676

  • Preceding prime number: 673
  • Following prime number: 677
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