Is 88 a prime number? What are the divisors of 88?

Is 88 a prime number?

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

For 88, the answer is: No, 88 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 88) is as follows: 1, 2, 4, 8, 11, 22, 44, 88.

To be 88 a prime number, it would have been required that 88 has only two divisors, i.e., itself and 1.

As a consequence:

  • 88 is a multiple of 1
  • 88 is a multiple of 2
  • 88 is a multiple of 4
  • 88 is a multiple of 8
  • 88 is a multiple of 11
  • 88 is a multiple of 22
  • 88 is a multiple of 44

To be 88 a prime number, it would have been required that 88 has only two divisors, i.e., itself and 1.

Is 88 a deficient number?

No, 88 is not a deficient number: to be deficient, 88 should have been such that 88 is larger than the sum of its proper divisors, i.e., the divisors of 88 without 88 itself (that is 1 + 2 + 4 + 8 + 11 + 22 + 44 = 92).

In fact, 88 is an abundant number; 88 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 11 + 22 + 44 = 92). The smallest abundant number is 12.

Parity of 88

88 is an even number, because it is evenly divisible by 2: 88 / 2 = 44.

Is 88 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 88 is about 9.381.

Thus, the square root of 88 is not an integer, and therefore 88 is not a square number.

What is the square number of 88?

The square of a number (here 88) is the result of the product of this number (88) by itself (i.e., 88 × 88); the square of 88 is sometimes called "raising 88 to the power 2", or "88 squared".

The square of 88 is 7 744 because 88 × 88 = 882 = 7 744.

As a consequence, 88 is the square root of 7 744.

Number of digits of 88

88 is a number with 2 digits.

What are the multiples of 88?

The multiples of 88 are all integers evenly divisible by 88, that is all numbers such that the remainder of the division by 88 is zero. There are infinitely many multiples of 88. The smallest multiples of 88 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 88 too, since 0 × 88 = 0
  • 88: indeed, 88 is a multiple of itself, since 88 is evenly divisible by 88 (we have 88 / 88 = 1, so the remainder of this division is indeed zero)
  • 176: indeed, 176 = 88 × 2
  • 264: indeed, 264 = 88 × 3
  • 352: indeed, 352 = 88 × 4
  • 440: indeed, 440 = 88 × 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 88). 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 9.381). 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 88

  • Preceding numbers: …86, 87
  • Following numbers: 89, 90

Nearest numbers from 88

  • Preceding prime number: 83
  • Following prime number: 89
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