Numberwise

153

153 is a narcissistic number — 1³ + 5³ + 3³ = 153 — and also the 17th triangular number.

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Where 153 fits

Where 153 fits: Mathematics, Related numbersMathematics: Triangular number, Narcissistic (Armstrong) number, Hexagonal number, Harshad (Niven) number. Related numbers: 17, 9474.MathematicsTriangular numberNarcissistic (Armstrong) nu…Hexagonal numberHarshad (Niven) numberRelated numbers179474153
153 connects to 2 worlds: mathematics, related numbers.

Why 153 is special

153 is the richest of the three-digit narcissistic numbers: raising each of its own digits to the power of three and adding them returns 153 itself, and it is simultaneously triangular (the sum of every whole number from 1 to 17). Separately, the Gospel of John's account of a miraculous catch specifies 153 fish, which has made the number a subject of long-standing commentary within Christian tradition.

153 connects to:

  • 17 is a multiple of
  • 9474 is associated with

Same number, different meanings

How 153 is understood across different contexts — never implying one meaning because of another.

153 is part of

Factors & digit properties

Divisors (6)
1, 3, 9, 17, 51, 153
Prime factorisation
3^2 × 17
Digit sum
9
Digital root
9

Representations

Decimal
153
Scientific notation
1.530 × 10^2

Roman numerals

C L I I I

Binary

1 0 0 1 1 0 0 1

1 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 153

Octal

2 3 1

2 × 64 + 3 × 8 + 1 × 1 = 153

Hexadecimal

9 9

9 × 16 + 9 × 1 = 153

Read as powers of two: 128 + 16 + 8 + 1 = 153.

In historical numeral systems

Egyptian

1 coil of rope, 5 hobbles, 3 strokes

1 × 100 + 5 × 10 + 3 × 1 = 153. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.

Babylonian

2 vertical wedges (sixties place), 3 corner wedges + 3 vertical wedges (units place)

2 × 60 + 33 = 153. Places are separated by a space on the tablet, with the higher place written first.

Greek (Ionic)

rho, then nu, then gamma, marked as a numeral

rho-nu-gamma + keraia

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

Hebrew numerals

qof, then nun, then gimel

qof-nun-gimel

qof (100) + nun (50) + gimel (3) = 153, written in descending order.

Maya

1 bar + 2 dots (upper, twenties place) over 2 bars + 3 dots (lower, units place)

7 × 20 + 13 = 153. 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

  • Triangular number
  • Deficient number
  • Narcissistic (Armstrong) number
  • Hexagonal number
  • Harshad (Niven) number

Related numbers & connections

Mathematical relationship
153 is 9 × 17 — and, relatedly, the 17th triangular number (the sum of 1 through 17).

153 is 9 × 17 — and, relatedly, the 17th triangular number (the sum of 1 through 17).

View 17
Connection
Both equal the sum of their own digits raised to the number of digits. 153 is the three-digit case and 9,474 the four-digit one.

Both equal the sum of their own digits raised to the number of digits. 153 is the three-digit case and 9,474 the four-digit one.

View 9474

Mathematically related

  • is a multiple of17
    why?

    Strength 0.50, confidence "high".

Other connections

  • is associated with9474
    why?

    Strength 0.50, confidence "high".

How is 153 connected to another number? →

History

  • The precision of the figure in John 21:11 has drawn commentary since antiquity. Jerome reported a claim that Greek zoologists recognised 153 species of fish, so the catch stood for all nations — the claim does not correspond to any surviving Greek source. Augustine derived it as the sum of 1 to 17. Modern scholarship generally treats these as later attempts to explain a detail whose original purpose is unrecoverable, and none has become the accepted reading.

    DisputedHistoryPeriod: 4th century CE onwards

Religion & belief

  • The Gospel of John (21:11) specifies that the disciples' catch numbered 153 fish — an unusually precise figure in the text that has attracted centuries of commentary within Christian tradition, with no single interpretation regarded as settled.

    DocumentedReligion & beliefCulture: Christian tradition

Mathematics

  • 153 = 1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120. Together with its narcissistic and triangular properties this makes 153 unusually crowded for a three-digit number, and the three facts are independent of one another rather than consequences of a single structure — which is why it turns up in recreational mathematics more often than numbers with a deeper single property.

    DocumentedMathematics
  • 153 is a narcissistic (Armstrong) number: the sum of the cubes of its own digits returns the number itself, 1³ + 5³ + 3³ = 1 + 125 + 27 = 153. It is also the 17th triangular number, the sum of every whole number from 1 to 17.

    DocumentedMathematics

Common questions

Why does the Gospel of John specify 153 fish?

Nobody knows, and the attempts to explain it are themselves the interesting part. Jerome reported a claim that Greek zoologists recognised 153 species of fish, so the catch stood for all nations — no surviving Greek source says that. Augustine derived it as the sum of 1 to 17. Modern scholarship generally treats these as later explanations of a detail whose original purpose is unrecoverable. The arithmetic is settled: 153 is the 17th triangular number, the sum of the cubes of its own digits, and 1! + 2! + 3! + 4! + 5!.

Is 153 a prime number?

No, 153 is not prime.

What are the factors of 153?

The factors of 153 are 1, 3, 9, 17, 51, 153.

What is 153 in Roman numerals?

153 in Roman numerals is CLIII.

About this page's data

Mathematical facts:computed directly from the number's value — nothing to source or verify externally.

Contextual records: 4 reviewer-confirmed records, sourced and reviewed before publication.

Last reviewed: 15 July 2026