Number reference
420 explained.
420: four hundred twenty, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- four hundred twenty
- Classification
- composite
- Factors
- 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
- Prime factorization
- 2 × 2 × 3 × 5 × 7
- Square root
- 20.493902
- Cube root
- 7.488872
- Binary
- 110100100
- Octal
- 644
- Hexadecimal
- 1A4
- Roman numeral
- CDXX
- Digit sum
- 6
- Digital root
- 6
What makes 420 notable
- Factor structure. 420 breaks down into 4 distinct primes (2, 3, 5, 7) and has 24 divisors in total, so it can be split into equal whole-number groups 22 ways beyond 1 and itself.
420 in everyday use
Four hundred twenty is a cultural code in two countries for two different reasons. In the United States it has been associated with cannabis since the 1970s, when a group of San Rafael high-school students used 4:20 as a meeting time; the usage spread through Grateful Dead circles and 20 April is now an informal day of observance. In India, Section 420 of the old Penal Code covered cheating, and calling someone a "420" means a swindler. Both meanings are widely understood and neither has anything to do with arithmetic.
The arithmetic is interesting anyway. 420 is 2² × 3 × 5 × 7, the smallest number divisible by every whole number from 1 to 7, and it has 24 divisors, as many as 360. It is pronic, being 20 × 21, and in degrees it is 360 + 60, a full turn plus a sixth of a turn. It is also the sum of four consecutive primes, 101 + 103 + 107 + 109, and its digit sum is 6.
Nearby numbers
How to read this page
The factor list shows every way 420 splits into equal whole-number groups — 24 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 420 for contexts that do not use decimal.
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