Is 121 a prime number? What are the divisors of 121?

Is 121 a prime number?

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

For 121, the answer is: No, 121 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 121) is as follows: 1, 11, 121.

To be 121 a prime number, it would have been required that 121 has only two divisors, i.e., itself and 1.

As a consequence:

  • 121 is a multiple of 1
  • 121 is a multiple of 11

To be 121 a prime number, it would have been required that 121 has only two divisors, i.e., itself and 1.

However, 121 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 121 = 11 x 11, where 11 is a prime number.

Is 121 a deficient number?

Yes, 121 is a deficient number, that is to say 121 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 121 without 121 itself (that is 1 + 11 = 12).

Parity of 121

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

Is 121 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 121 is 11.

Therefore, the square root of 121 is an integer, and as a consequence 121 is a perfect square.

As a consequence, 11 is the square root of 121.

What is the square number of 121?

The square of a number (here 121) is the result of the product of this number (121) by itself (i.e., 121 × 121); the square of 121 is sometimes called "raising 121 to the power 2", or "121 squared".

The square of 121 is 14 641 because 121 × 121 = 1212 = 14 641.

As a consequence, 121 is the square root of 14 641.

Number of digits of 121

121 is a number with 3 digits.

What are the multiples of 121?

The multiples of 121 are all integers evenly divisible by 121, that is all numbers such that the remainder of the division by 121 is zero. There are infinitely many multiples of 121. The smallest multiples of 121 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 121 too, since 0 × 121 = 0
  • 121: indeed, 121 is a multiple of itself, since 121 is evenly divisible by 121 (we have 121 / 121 = 1, so the remainder of this division is indeed zero)
  • 242: indeed, 242 = 121 × 2
  • 363: indeed, 363 = 121 × 3
  • 484: indeed, 484 = 121 × 4
  • 605: indeed, 605 = 121 × 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 121). 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 11). 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 121

  • Preceding numbers: …119, 120
  • Following numbers: 122, 123

Nearest numbers from 121

  • Preceding prime number: 113
  • Following prime number: 127
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