120 (number)
natural number
120 is a natural number. It is before 121 and after 119. It reads as one hundred [and] twenty.
| ||||
|---|---|---|---|---|
| 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 | |||
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 the first highly composite number.[1] It is also superior highly composite.
- 120 is superabundant[2] and a colossally abundant number.[3]
- 120 is sparsely totient.[4]
- 120 is the smallest number to appear six times in Pascal's triangle.
- 120 is a Harshad number in base 10.[5]
- 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.[6]
References
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 135
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