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Wolfram Language & System Documentation Center
IntegerDigits
  • See Also
    • FromDigits
    • IntegerString
    • NumberExpand
    • DigitCount
    • IntegerLength
    • DigitSum
    • NumberDecompose
    • RealDigits
    • NumberDigit
    • BaseForm
    • NumberForm
    • RomanNumeral
    • IntegerReverse
    • PalindromeQ
    • IntegerExponent
    • IntegerPart
    • ContinuedFraction
    • Tuples
    • BitAnd
    • BitOr
    • BitLength
  • Related Guides
    • Number Digits
    • Constructing Lists
    • Representation of Numbers
    • Numerical Evaluation & Precision
    • Discrete Mathematics
    • Number Theoretic Functions
    • Additive Number Theory
    • Number Theory
    • Integer Functions
    • Mathematical Functions
    • Atomic Elements of Expressions
  • Tech Notes
    • Digits in Numbers
    • Integer and Number Theoretic Functions
    • Implementation notes: Numerical and Related Functions
    • See Also
      • FromDigits
      • IntegerString
      • NumberExpand
      • DigitCount
      • IntegerLength
      • DigitSum
      • NumberDecompose
      • RealDigits
      • NumberDigit
      • BaseForm
      • NumberForm
      • RomanNumeral
      • IntegerReverse
      • PalindromeQ
      • IntegerExponent
      • IntegerPart
      • ContinuedFraction
      • Tuples
      • BitAnd
      • BitOr
      • BitLength
    • Related Guides
      • Number Digits
      • Constructing Lists
      • Representation of Numbers
      • Numerical Evaluation & Precision
      • Discrete Mathematics
      • Number Theoretic Functions
      • Additive Number Theory
      • Number Theory
      • Integer Functions
      • Mathematical Functions
      • Atomic Elements of Expressions
    • Tech Notes
      • Digits in Numbers
      • Integer and Number Theoretic Functions
      • Implementation notes: Numerical and Related Functions

IntegerDigits[n]

gives a list of the decimal digits in the integer n.

IntegerDigits[n,b]

gives a list of the base b digits in the integer n.

IntegerDigits[n,b,len]

pads the list on the left with zeros to give a list of length len.

IntegerDigits[n,MixedRadix[blist]]

uses the mixed radix with list of bases blist.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • FromDigits
    • IntegerString
    • NumberExpand
    • DigitCount
    • IntegerLength
    • DigitSum
    • NumberDecompose
    • RealDigits
    • NumberDigit
    • BaseForm
    • NumberForm
    • RomanNumeral
    • IntegerReverse
    • PalindromeQ
    • IntegerExponent
    • IntegerPart
    • ContinuedFraction
    • Tuples
    • BitAnd
    • BitOr
    • BitLength
  • Related Guides
    • Number Digits
    • Constructing Lists
    • Representation of Numbers
    • Numerical Evaluation & Precision
    • Discrete Mathematics
    • Number Theoretic Functions
    • Additive Number Theory
    • Number Theory
    • Integer Functions
    • Mathematical Functions
    • Atomic Elements of Expressions
  • Tech Notes
    • Digits in Numbers
    • Integer and Number Theoretic Functions
    • Implementation notes: Numerical and Related Functions
    • See Also
      • FromDigits
      • IntegerString
      • NumberExpand
      • DigitCount
      • IntegerLength
      • DigitSum
      • NumberDecompose
      • RealDigits
      • NumberDigit
      • BaseForm
      • NumberForm
      • RomanNumeral
      • IntegerReverse
      • PalindromeQ
      • IntegerExponent
      • IntegerPart
      • ContinuedFraction
      • Tuples
      • BitAnd
      • BitOr
      • BitLength
    • Related Guides
      • Number Digits
      • Constructing Lists
      • Representation of Numbers
      • Numerical Evaluation & Precision
      • Discrete Mathematics
      • Number Theoretic Functions
      • Additive Number Theory
      • Number Theory
      • Integer Functions
      • Mathematical Functions
      • Atomic Elements of Expressions
    • Tech Notes
      • Digits in Numbers
      • Integer and Number Theoretic Functions
      • Implementation notes: Numerical and Related Functions

IntegerDigits

IntegerDigits[n]

gives a list of the decimal digits in the integer n.

IntegerDigits[n,b]

gives a list of the base b digits in the integer n.

IntegerDigits[n,b,len]

pads the list on the left with zeros to give a list of length len.

IntegerDigits[n,MixedRadix[blist]]

uses the mixed radix with list of bases blist.

Details

  • IntegerDigits gives the most significant digit first, as in standard positional notation.
  • IntegerDigits[n] discards the sign of n.
  • If len is less than the number of digits in n, then the len least significant digits are returned.
  • IntegerDigits[0] gives {0}.
  • FromDigits can be used as the inverse of IntegerDigits.

Examples

open all close all

Basic Examples  (3)

Find digits in base 10:

Find digits in base 2:

Find digits in a mixed radix system:

Scope  (8)

Bases larger than 10 can be used:

IntegerDigits threads itself over elements of lists:

Find the digits of 7 in different bases:

By default, IntegerDigits includes no leading zeros:

Pad all digit lists to be length 3:

Find only the last 4 digits:

Find digits using a MixedRadix specification:

Find only the last 2 digits:

Applications  (4)

Leading digits of factorials:

ChampernowneNumber has a decimal expansion that is a concatenation of consecutive integers:

Compare to ChampernowneNumber:

Cantor set construction:

Construct a van der Corput sequence:

The sequence forms a dense set that is equidistributed in the unit interval:

Build a Halton sequence:

Illustrate low-discrepancy property of the sequence:

Properties & Relations  (4)

Find all combinations of 3 binary digits:

Pad digit lists to be the same length:

The sign is ignored:

Express an amount of seconds in hours, minutes, and seconds:

It can also be obtained with NumberDecompose:

Perform the same computation using Quantity objects:

Neat Examples  (1)

Leading digits of factorials in base 100:

See Also

FromDigits  IntegerString  NumberExpand  DigitCount  IntegerLength  DigitSum  NumberDecompose  RealDigits  NumberDigit  BaseForm  NumberForm  RomanNumeral  IntegerReverse  PalindromeQ  IntegerExponent  IntegerPart  ContinuedFraction  Tuples  BitAnd  BitOr  BitLength

Function Repository: NthDigit  GrayCode  ToNegabinary  BinaryCodedTernary

Tech Notes

    ▪
  • Digits in Numbers
  • ▪
  • Integer and Number Theoretic Functions
  • ▪
  • Implementation notes: Numerical and Related Functions

Related Guides

    ▪
  • Number Digits
  • ▪
  • Constructing Lists
  • ▪
  • Representation of Numbers
  • ▪
  • Numerical Evaluation & Precision
  • ▪
  • Discrete Mathematics
  • ▪
  • Number Theoretic Functions
  • ▪
  • Additive Number Theory
  • ▪
  • Number Theory
  • ▪
  • Integer Functions
  • ▪
  • Mathematical Functions
  • ▪
  • Atomic Elements of Expressions

Related Links

  • MathWorld
  • An Elementary Introduction to the Wolfram Language : More about Numbers
  • An Elementary Introduction to the Wolfram Language : Operations on Lists
  • An Elementary Introduction to the Wolfram Language : Pure Anonymous Functions
  • An Elementary Introduction to the Wolfram Language : Writing Good Code
  • NKS|Online  (A New Kind of Science)

History

Introduced in 1991 (2.0) | Updated in 1996 (3.0) ▪ 2003 (5.0) ▪ 2015 (10.2)

Wolfram Research (1991), IntegerDigits, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerDigits.html (updated 2015).

Text

Wolfram Research (1991), IntegerDigits, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerDigits.html (updated 2015).

CMS

Wolfram Language. 1991. "IntegerDigits." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/IntegerDigits.html.

APA

Wolfram Language. (1991). IntegerDigits. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntegerDigits.html

BibTeX

@misc{reference.wolfram_2025_integerdigits, author="Wolfram Research", title="{IntegerDigits}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/IntegerDigits.html}", note=[Accessed: 01-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_integerdigits, organization={Wolfram Research}, title={IntegerDigits}, year={2015}, url={https://reference.wolfram.com/language/ref/IntegerDigits.html}, note=[Accessed: 01-May-2026]}

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