120 (number)

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

← 119 120 121 →
← 120 121 122 123 124 125 126 127 128 129 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred twenty
Ordinal	120th (one hundred twentieth)
Factorization	23× 3 × 5
Divisors	1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Greek numeral	ΡΚ´
Roman numeral	CXX
Binary	11110002
Ternary	111103
Quaternary	13204
Quinary	4405
Senary	3206
Octal	1708
Duodecimal	A012
Hexadecimal	7816
Vigesimal	6020
Base 36	3C36

The 120-cell (or hecatonicosachoron) is a convex regular 4-polytope consisting of 120 dodecahedral cells

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 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