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IntegerExponent[n,b]

gives the highest power of b that divides n.

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IntegerExponent

IntegerExponent[n,b]

gives the highest power of b that divides n.

Details

Examples

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Basic Examples  (3)

The number of trailing zeros:

Wolfram Language code: IntegerExponent[1230000]

The highest power of 2:

Wolfram Language code: IntegerExponent[2 ^ 10 + 2 ^ 7, 2]
Wolfram Language code: IntegerExponent[2^^10010000, 2]

Plot it:

Wolfram Language code: DiscretePlot[IntegerExponent[n, 2], {n, 2 ^ 7 - 1}]

Applications  (2)

Number of trailing zeros in factorials:

Wolfram Language code: Table[IntegerExponent[n!], {n, 50}]

Powers of 2 in successive integers:

Wolfram Language code: IntegerExponent[Range[50], 2]
Wolfram Language code: ListPlot[IntegerExponent[Range[256], 2]]

Properties & Relations  (1)

Find the highest power of 2 that appears in the factors of a number:

Wolfram Language code: FactorInteger[2524]
Wolfram Language code: IntegerExponent[2524, 2]

Neat Examples  (1)

A "formula" for DigitCount:

Wolfram Language code: Table[n - IntegerExponent[n!, 2], {n, 30}]
Wolfram Language code: Table[DigitCount[n, 2, 1], {n, 30}]
Wolfram Research (1999), IntegerExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerExponent.html.

Text

Wolfram Research (1999), IntegerExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerExponent.html.

CMS

Wolfram Language. 1999. "IntegerExponent." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/IntegerExponent.html.

APA

Wolfram Language. (1999). IntegerExponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntegerExponent.html

BibTeX

@misc{reference.wolfram_2026_integerexponent, author="Wolfram Research", title="{IntegerExponent}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/IntegerExponent.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_integerexponent, organization={Wolfram Research}, title={IntegerExponent}, year={1999}, url={https://reference.wolfram.com/language/ref/IntegerExponent.html}, note=[Accessed: 12-June-2026]}