Numberwise

2,048

2048 is 2¹¹, and the name of the sliding-tile puzzle game where players combine tiles to reach 2048.

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Where 2,048 fits

Where 2,048 fits: Mathematics, Related numbersMathematics: Powerful number. Related numbers: 1024, 4096.MathematicsPowerful numberRelated numbers102440962,048
2,048 connects to 2 worlds: mathematics, related numbers.

Why 2,048 is special

2048 is a power of two that became a game: the 2014 puzzle 2048 asks players to merge matching tiles, doubling each time, until one tile reaches 2048 — so the target is not arbitrary but the eleventh doubling of 2. It is also twice 1024, the historical kilobyte.

2,048 connects to:

  • 1024 is a multiple of
  • 4096 is a factor of
  • powers of two appears in

Same number, different meanings

How 2,048 is understood across different contexts — never implying one meaning because of another.

2,048 is part of

Factors & digit properties

Divisors (12)
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048
Prime factorisation
2^11
Digit sum
14
Digital root
5

Representations

Decimal
2048
Scientific notation
2.048 × 10^3

Roman numerals

M M X L V I I I

MMXLVIII uses the subtractive pair XL: ten before fifty — fifty minus ten.

Binary

1 0 0 0 0 0 0 0 0 0 0 0

1 × 2,048 + 0 × 1,024 + 0 × 512 + 0 × 256 + 0 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 2,048

Octal

4 0 0 0

4 × 512 + 0 × 64 + 0 × 8 + 0 × 1 = 2,048

Hexadecimal

8 0 0

8 × 256 + 0 × 16 + 0 × 1 = 2,048

Read as powers of two: 2,048 = 2,048.

In historical numeral systems

Egyptian

2 lotuses, 4 hobbles, 8 strokes

2 × 1,000 + 4 × 10 + 8 × 1 = 2,048. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.

Babylonian

3 corner wedges + 4 vertical wedges (sixties place), 8 vertical wedges (units place)

34 × 60 + 8 = 2048. Places are separated by a space on the tablet, with the higher place written first.

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

  • Deficient number
  • Powerful number

Related numbers & connections

Mathematical relationship
2048 is exactly twice 1024 — the next doubling of two, and the reason the 2048 game's target follows from 1024.

2048 is exactly twice 1024 — the next doubling of two, and the reason the 2048 game's target follows from 1024.

View 1024
Documented appearance
2¹¹ — twice 1024, and the target that gives the puzzle game its name.

2¹¹ — twice 1024, and the target that gives the puzzle game its name.

Mathematically related

  • is a multiple of1024
    why?

    Strength 0.50, confidence "high".

  • is a factor of4096
    why?

    Strength 0.50, confidence "high".

Numbers Around Us

  • appears inPowers of two
    why?

    Strength 0.50, confidence "high".

How is 2,048 connected to another number? →

Everyday life

  • 2,048 is the number of 512-byte logical sectors in a 1 MiB alignment boundary, which is why disk partitioning tools now start the first partition at sector 2048 rather than at 63 as older ones did. The change was made so that partitions align with the 4,096-byte physical sectors of Advanced Format drives; a misaligned partition forces the drive to read and rewrite two physical sectors for every logical write, with a measurable cost in performance and wear.

    DocumentedEveryday life

Technology & computing

  • 2048 bits is the minimum RSA key length approved for general use by NIST, and the length most public certificates still use; 1024 was withdrawn in 2013 and 3072 is the recommendation for protection beyond 2030. Key lengths are quoted with an expiry rather than as fixed advice because the threat is factoring capability, which improves — and because a key generated today may still be protecting something in a decade.

    DocumentedTechnology & computing

Mathematics

  • 2,048 = 2¹¹, and the game's rule set makes that visible: tiles start at 2 and each merge doubles, so reaching the 2048 tile requires exactly eleven successful doublings and the board's numbers are the powers of two in order. The target was chosen because eleven doublings is difficult but not impossible on a 4 × 4 grid — the game continues past it, and 4096 and 8192 are reachable.

    DocumentedMathematics
  • 2048 is 2¹¹, and exactly twice 1024.

    DocumentedMathematics

Media & popular culture

  • 2048 is a sliding-tile puzzle game released in 2014 by Gabriele Cirulli, in which players merge matching numbered tiles — each merge doubling the value — with the goal of producing a 2048 tile.

    DocumentedMedia & popular culturePeriod: 2014

Common questions

Why is the game called 2048?

Because tiles start at 2 and every merge doubles, so reaching a 2048 tile takes exactly eleven successful doublings — 2,048 is 2¹¹. The target was picked as hard but achievable on a 4 × 4 grid; the game continues past it, and 4096 and 8192 are reachable.

Is 2,048 a prime number?

No, 2,048 is not prime.

What are the factors of 2,048?

The factors of 2,048 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048.

What is 2,048 in Roman numerals?

2,048 in Roman numerals is MMXLVIII. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be MMXXXXVIII, 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: 5 reviewer-confirmed records, sourced and reviewed before publication.

Last reviewed: 15 July 2026