Basic Examples (1) 

Verify the result claimed in the Details section:

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Scope (2) 

MultiplicativeDigitalRoot threads elementwise over lists:

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Compute the multiplicative digital root of the first 100 integers (OEIS A031347):

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Properties and Relations (4) 

The result returned by MultiplicativeDigitalRoot can be manually computed using NestWhileList:

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The multiplicative digital root of an integer can also be manually computed with no high-level functions:

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Because testint3 is a single-digit integer, the process terminates here, and because testint3 equals 8, the multiplicative digital root of testint1=1234 is equal to 8:

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The number of iterations required to reach the end of the digit multiplication process is called the multiplicative persistence and is returned by the resource function MultiplicativePersistence:

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The additive analogue of the multiplicative digital root is called the additive digital root and is returned by the resource function AdditiveDigitalRoot:

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Possible Issues (1) 

MultiplicativeDigitalRoot requires its input to be non-negative:

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Neat Examples (1) 

Create a OEIS-themed table showing which integers have the same multiplicative digital root. This partially reproduces a cool result from the associated MathWorld article:

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