120 (number)

120 is a natural number. It is before 121 and after 119. It reads as one hundred [and] twenty. 

 In mathematics 

 Subsets 

 It is also the fifteenth triangular number. It is also the sum of the first eight triangular numbers. This makes it a tetrahedral number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers. It is the eighth hexagonal number.
 120 is a highly composite number. It is also superior highly composite.
 120 is superabundant and a colossally abundant number. 
 120 is sparsely totient.
 120 is the smallest number to appear six times in Pascal's triangle.
 120 is a Harshad number in base 10.
 120 is the largest known integer in Pierre de Fermat's modified Diophantine equation(1, 3, 8 and 120).

 Relations between numbers, equations and shapes 

 120 is the factorial of 5.
 120's adjacent numbers are 119 and 121. 120 is the first multiple of 6 (number) to not have an adjacent prime number.
 The sum of its factors (including one and itself) equal 360. 360 is three times 120.
 120 is the sum a twin prime pair (59 + 61). It is also the sum of four prime numbers in a row (23 + 29 + 31 + 37). It is the sum of four powers of two in a row (8 + 16 + 32 + 64). Finally, it is the sum of four powers of 3 (3 + 9 + 27 + 81).
 120 is divisible by the number of prime numbers below it(there are 30 prime numbers below 120). 
 The sum of Euler's totient function φ(x) of its first nineteen integers is 120.
 Each angles of a regular hexagon (one where all sides and all angles are equal) are all 120 degrees.

 In science 

 120 is the atomic number of unbinilium.
 In electrical engineering, each line of the three-phase system is 120 degrees away from each other.

 In religion 

 The Temple building(in II Chronicles 3:4) is 120 cubits tall.
 Moses dies at age 120(Deut. 34:7). To wish for someone to have a long life, it is popular to say, "Live until 120" in the Jewish religion.
 The Queen of Sheba gave Solomon 120 talents of gold. (I Kings 10:10)
 King Darius put 120 princes in his kingdom. (Daniel 6:2)
 120 shekels worth of gold spoons are offered to every tribal prince in Israel (Num. 7:86).
 In astrology, a trine is when two planets in a person's chart are 120 degrees away from each other. This gives the person good luck.

 References 

 Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 135

Category:Integers