Is 98 a prime number? What are the divisors of 98?

Is 98 a prime number?

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

For 98, the answer is: No, 98 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 98) is as follows: 1, 2, 7, 14, 49, 98.

To be 98 a prime number, it would have been required that 98 has only two divisors, i.e., itself and 1.

As a consequence:

  • 98 is a multiple of 1
  • 98 is a multiple of 2
  • 98 is a multiple of 7
  • 98 is a multiple of 14
  • 98 is a multiple of 49

To be 98 a prime number, it would have been required that 98 has only two divisors, i.e., itself and 1.

Is 98 a deficient number?

Yes, 98 is a deficient number, that is to say 98 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 98 without 98 itself (that is 1 + 2 + 7 + 14 + 49 = 73).

Parity of 98

98 is an even number, because it is evenly divisible by 2: 98 / 2 = 49.

Is 98 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 98 is about 9.899.

Thus, the square root of 98 is not an integer, and therefore 98 is not a square number.

What is the square number of 98?

The square of a number (here 98) is the result of the product of this number (98) by itself (i.e., 98 × 98); the square of 98 is sometimes called "raising 98 to the power 2", or "98 squared".

The square of 98 is 9 604 because 98 × 98 = 982 = 9 604.

As a consequence, 98 is the square root of 9 604.

Number of digits of 98

98 is a number with 2 digits.

What are the multiples of 98?

The multiples of 98 are all integers evenly divisible by 98, that is all numbers such that the remainder of the division by 98 is zero. There are infinitely many multiples of 98. The smallest multiples of 98 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 98 too, since 0 × 98 = 0
  • 98: indeed, 98 is a multiple of itself, since 98 is evenly divisible by 98 (we have 98 / 98 = 1, so the remainder of this division is indeed zero)
  • 196: indeed, 196 = 98 × 2
  • 294: indeed, 294 = 98 × 3
  • 392: indeed, 392 = 98 × 4
  • 490: indeed, 490 = 98 × 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 98). 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 9.899). 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 98

  • Preceding numbers: …96, 97
  • Following numbers: 99, 100

Nearest numbers from 98

  • Preceding prime number: 97
  • Following prime number: 101
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