420 (number)
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|---|---|---|---|---|
| Cardinal | four hundred twenty | |||
| Ordinal | 420th (four hundred twentieth) | |||
| Factorization | 22 × 3 × 5 × 7 | |||
| Divisors | 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 | |||
| Greek numeral | ΥΚ´ | |||
| Roman numeral | CDXX, cdxx | |||
| Binary | 1101001002 | |||
| Ternary | 1201203 | |||
| Senary | 15406 | |||
| Octal | 6448 | |||
| Duodecimal | 2B012 | |||
| Hexadecimal | 1A416 | |||
420 (four hundred [and] twenty) is the natural number following 419 and preceding 421.[1]
In mathematics
[edit]420 is a zero of the Mertens function,[2] a sparsely totient number,[3] a pronic number,[1][4] a balanced number,[5] a largely composite number,[6] a unitary harmonic number,[7][8] an infinitary harmonic number.[9][10] and a cluster prime.[11]
420 is the number of minimal covers on 7 objects with 6 members.[12]
Divisors
[edit]The divisors of 420 is 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420.[1][13] Because the first seven divisors is going from 1 to 7, it is the smallest number that is divisible by 1 through 7.[14][15]
In other fields
[edit]420 (pronounced four-twenty) is a cannabis culture slang for cannabis consumption.[16]
References
[edit]- 1 2 3 Vanovschi, Vitalii. "Properties of the number 420". www.numberempire.com. Retrieved 2026-09-16.
- ↑ Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers n such that Mertens' function is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Hagis, Jr., Peter; Lord, Graham (August 1975). "Unitary Harmonic Numbers" (PDF). Proceedings of the American Mathematical Society. 51 (1): 1–7.
- ↑ Sloane, N. J. A. (ed.). "Sequence A006086 (Unitary harmonic numbers (those for which the unitary harmonic mean is an integer))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Hagis, Peter; Cohen, Graeme L. (February 1990). "Infinitary harmonic numbers". Bulletin of the Australian Mathematical Society. 41 (1): 151–158. doi:10.1017/S0004972700017949. ISSN 0004-9727.
- ↑ Sloane, N. J. A. (ed.). "Sequence A063947 (Infinitary harmonic numbers: harmonic mean of infinitary divisors is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Weisstein, Eric W. "Cluster Prime". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-16.
- ↑ Weisstein, Eric W. "Minimal Cover". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 2026-09-16.
- ↑ "Factors of 420 - Find Prime Factorization/Factors of 420". Cuemath. Retrieved 2026-09-16.
- ↑ Friedman, Erich. "What's Special About This Number?". erich-friedman.github.io. Retrieved 2026-09-16.
- ↑ Sloane, N. J. A. (ed.). "Sequence A003418 (Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ "Stoner Chic Traces Origin To San Rafael – Snickering high schoolers brought '420' into lexicon". San Francisco Chronicle. April 20, 2000. Archived from the original on May 27, 2012. Retrieved April 4, 2012.
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