Is 120 a prime number? What are the divisors of 120?

Is 120 a prime number?

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

For 120, the answer is: No, 120 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 120) is as follows: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

To be 120 a prime number, it would have been required that 120 has only two divisors, i.e., itself and 1.

As a consequence:

  • 120 is a multiple of 1
  • 120 is a multiple of 2
  • 120 is a multiple of 3
  • 120 is a multiple of 4
  • 120 is a multiple of 5
  • 120 is a multiple of 6
  • 120 is a multiple of 8
  • 120 is a multiple of 10
  • 120 is a multiple of 12
  • 120 is a multiple of 15
  • 120 is a multiple of 20
  • 120 is a multiple of 24
  • 120 is a multiple of 30
  • 120 is a multiple of 40
  • 120 is a multiple of 60

To be 120 a prime number, it would have been required that 120 has only two divisors, i.e., itself and 1.

Is 120 a deficient number?

No, 120 is not a deficient number: to be deficient, 120 should have been such that 120 is larger than the sum of its proper divisors, i.e., the divisors of 120 without 120 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 = 240).

In fact, 120 is an abundant number; 120 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 = 240). The smallest abundant number is 12.

Parity of 120

120 is an even number, because it is evenly divisible by 2: 120 / 2 = 60.

Is 120 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 120 is about 10.954.

Thus, the square root of 120 is not an integer, and therefore 120 is not a square number.

What is the square number of 120?

The square of a number (here 120) is the result of the product of this number (120) by itself (i.e., 120 × 120); the square of 120 is sometimes called "raising 120 to the power 2", or "120 squared".

The square of 120 is 14 400 because 120 × 120 = 1202 = 14 400.

As a consequence, 120 is the square root of 14 400.

Number of digits of 120

120 is a number with 3 digits.

What are the multiples of 120?

The multiples of 120 are all integers evenly divisible by 120, that is all numbers such that the remainder of the division by 120 is zero. There are infinitely many multiples of 120. The smallest multiples of 120 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 120 too, since 0 × 120 = 0
  • 120: indeed, 120 is a multiple of itself, since 120 is evenly divisible by 120 (we have 120 / 120 = 1, so the remainder of this division is indeed zero)
  • 240: indeed, 240 = 120 × 2
  • 360: indeed, 360 = 120 × 3
  • 480: indeed, 480 = 120 × 4
  • 600: indeed, 600 = 120 × 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 120). 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 10.954). 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 120

  • Preceding numbers: …118, 119
  • Following numbers: 121, 122

Nearest numbers from 120

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