ⓘ 120 (number)


ⓘ 120 (number)

120, read as one hundred twenty, is the natural number following 119 and preceding 121.

In the Germanic languages, the number 120 was also formerly known as "one hundred". This "hundred" of six score is now obsolete, but is described as the long hundred or great hundred in historical contexts.


1. In mathematics

120 is the factorial of 5 and one less than a square, making 5, 11 a Brown number pair. 120 is the sum of a twin prime pair 59 + 61 and the sum of four consecutive prime numbers 23 + 29 + 31 + 37, four consecutive powers of 2 8 + 16 + 32 + 64, and four consecutive powers of 3 + 9 + 27 + 81. It is highly composite, superabundant, and colossally abundant number, with its 16 divisors being more than any number lower than it has, and it is also the smallest number to have exactly that many divisors. It is also a sparsely totient number. 120 is the smallest number to appear six times in Pascals triangle. 120 is also the smallest multiple of 6 with no adjacent prime number, being adjacent to 119 = 7 × 17 and 121 = 11 2.

It is the eighth hexagonal number and the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers.

120 is the first multiply perfect number of order three a 3-perfect or triperfect number. The sum of its factors including one and itself sum to 360; exactly three times 120. Note that perfect numbers are order two 2-perfect by the same definition.

120 is divisible by the number of primes below it, 30 in this case. However, there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number.

The sum of Eulers totient function φx over the first nineteen integers is 120.

120 figures in Pierre de Fermats modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that multiplied with any of the other numbers in the sequence yields a number that is one less than a square. Leonhard Euler also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, 777480 / 2879 2.

The internal angles of a regular hexagon one where all sides and all angles are equal are all 120 degrees.

120 is a Harshad number in base 10.


2. In religion

  • By extension, in Jewish tradition, to wish someone a long life, one says, "Live until 120"
  • The cubits of the height of the Temple building II Chronicles 3:4
  • The age at which Moses died Deut. 34:7.
  • The summed weight in shekels of the gold spoons offered by each tribal prince of Israel Num. 7:86.
  • In astrology, when two planets in a persons chart are 120 degrees apart from each other, this is called a trine. This is supposed to bring good luck in the persons life.
  • The number of Men of the Great Assembly who canonized the Books of the Tanakh and formulated the Jewish prayers
  • The number of talents of gold that the Queen of Sheba gave to Solomon in tribute I Kings 10:10
  • The number of princes King Darius set over his kingdom Daniel 6:2

3. In other fields

120 is also:

  • In the US Army, a common diameter for a mortar in mm M120.
  • The medical telephone number in China
  • In Austria, the telephone number "to report a car breakdown on the highway.
  • The Israeli national legislature, the Knesset, has 120 seats.
  • 120 film, a 2008 Turkish film
  • China Airlines Flight 120
  • 120 film is a medium format film developed by Kodak.
  • TT scale, a scale for model trains, is 1:120.