840
840 is a highly composite number with 32 divisors.
- Even
- Composite
Where 840 fits
Why 840 is special
Numbers like this divide evenly in many ways, which is why they are chosen for things that must be split repeatedly — 60 seconds, 360 degrees, 12 inches. 840 is the smallest number divisible by all of 1 to 8.
Factors & digit properties
- Divisors (32)
- 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
- Prime factorisation
- 2^3 × 3 × 5 × 7
- Digit sum
- 12
- Digital root
- 3
Representations
- Decimal
- 840
- Scientific notation
- 8.400 × 10^2
Roman numerals
D C C C X L
DCCCXL uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 1 0 1 0 0 1 0 0 0
1 × 512 + 1 × 256 + 0 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 840
Octal
1 5 1 0
1 × 512 + 5 × 64 + 1 × 8 + 0 × 1 = 840
Hexadecimal
3 4 8
3 × 256 + 4 × 16 + 8 × 1 = 840
Read as powers of two: 512 + 256 + 64 + 8 = 840.
In historical numeral systems
Egyptian
8 coils of rope, 4 hobbles
8 × 100 + 4 × 10 = 840. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
1 corner wedge + 4 vertical wedges (sixties place), empty units place
14 × 60 + 0 = 840. Places are separated by a space on the tablet, with the higher place written first. The second place is empty, and this is precisely the case the early system could not write unambiguously — the same wedges alone would also read as 1.
Greek (Ionic)
omega, then mu, marked as a numeral
omega-mu + keraia
omega + mu written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
tav, then tav, then mem
tav-tav-mem
tav (400) + tav (400) + mem (40) = 840, written in descending order.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Abundant number
- Highly composite number
- Harshad (Niven) number
Mathematics
840 is the smallest number divisible by each of 1 to 8, which is why it appears wherever a quantity must be split many ways without remainder. It is the same reasoning that put 60 minutes in an hour and 360 degrees in a circle, carried further.
DocumentedMathematics
Common questions
Is 840 a prime number?
No, 840 is not prime.
What are the factors of 840?
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
What is 840 in Roman numerals?
840 in Roman numerals is DCCCXL. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be DCCCXXXX, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026