Numberwise

284

284 is the partner of 220 in the smallest amicable pair.

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Where 284 fits

Where 284 fits: Related numbersRelated numbers: 220.Related numbers220284
284 connects to 1 world: related numbers.

Why 284 is special

Its proper divisors sum to 220, whose divisors sum back to 284. No further pair was found for over a thousand years after these two, until Fermat and Descartes each produced one in the seventeenth century.

Factors & digit properties

Divisors (6)
1, 2, 4, 71, 142, 284
Prime factorisation
2^2 × 71
Digit sum
14
Digital root
5

Representations

Decimal
284
Scientific notation
2.840 × 10^2

Roman numerals

C C L X X X I V

CCLXXXIV uses the subtractive pair IV: one before five — five minus one.

Binary

1 0 0 0 1 1 1 0 0

1 × 256 + 0 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 1 × 8 + 1 × 4 + 0 × 2 + 0 × 1 = 284

Octal

4 3 4

4 × 64 + 3 × 8 + 4 × 1 = 284

Hexadecimal

1 1 c

1 × 256 + 1 × 16 + c × 1 = 284

Read as powers of two: 256 + 16 + 8 + 4 = 284.

In historical numeral systems

Egyptian

2 coils of rope, 8 hobbles, 4 strokes

2 × 100 + 8 × 10 + 4 × 1 = 284. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.

Babylonian

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

4 × 60 + 44 = 284. Places are separated by a space on the tablet, with the higher place written first.

Greek (Ionic)

sigma, then pi, then delta, marked as a numeral

sigma-pi-delta + keraia

sigma + pi + delta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.

Hebrew numerals

resh, then pe, then dalet

resh-pe-dalet

resh (200) + pe (80) + dalet (4) = 284, written in descending order.

Maya

2 bars + 4 dots (upper, twenties place) over 4 dots (lower, units place)

14 × 20 + 4 = 284. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.

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

Related numbers & connections

Shared classification
The smallest amicable pair: each number's proper divisors sum to the other. Known to the Pythagoreans and unmatched by any second pair for over a thousand years.

The smallest amicable pair: each number's proper divisors sum to the other. Known to the Pythagoreans and unmatched by any second pair for over a thousand years.

View 220

Shares a distinctive class

  • is associated with220
    why?

    Strength 0.50, confidence "high".

How is 284 connected to another number? →

History

  • The ninth-century mathematician Thābit ibn Qurra gave a rule that generates amicable pairs from primes of a particular form, and 220/284 is the case it produces first. The rule was rediscovered in Europe centuries later, and the two further pairs it yields — 17,296/18,416 and 9,363,584/9,437,056 — were found by Fermat and Descartes respectively, which is why the seventeenth-century 'discoveries' were in fact recoveries of a method already recorded in Arabic.

    DocumentedHistoryCulture: Arabic mathematical traditionPeriod: 9th century onwards

Mathematics

  • 284 = 2² × 71, so its proper divisors are only 1, 2, 4, 71 and 142 — five of them, against 220's eleven. The pair works because a number with few large divisors and a number with many small ones can arrive at each other's totals, and that asymmetry is typical: in almost every known amicable pair the two members have markedly different factorisations.

    DocumentedMathematics
  • 284's divisors sum to 220, completing the pair. No further amicable pair was found for more than a thousand years after these two were known, until Fermat and Descartes each produced one in the seventeenth century.

    DocumentedMathematics

Common questions

Is 284 a prime number?

No, 284 is not prime.

What are the factors of 284?

The factors of 284 are 1, 2, 4, 71, 142, 284.

What is 284 in Roman numerals?

284 in Roman numerals is CCLXXXIV. IV is subtractive: one before five — five minus one. Written additively it would be CCLXXXIIII, 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: 3 reviewer-confirmed records, sourced and reviewed before publication.

Last reviewed: 15 July 2026