Digit Sum | Digit Sum below Value | Base-k Digit Sum | Weighted Digit Sum | Digit Product | Triangular Number
Calculate Digit Product and Multiplicative Digital Root
The digit product is the product (multiplication) of the individual digits of a natural number. To calculate, just type or paste any text with numbers into the field and press Calculate digit product. Characters, which aren't numbers, are counted, but ignored for the digit product and root. Minus signs are also ignored. For the multiplicative digital root, the digit product is executed until the result is one-digit. The number of steps for this is called multiplicative persistence.
Examples: the digit product of 1234 = 1*2*3*4 = 24. The digit product of 679 is 378, its multiplicative digital root is 6 with the multiplicative persistence 5.
Like the digit sum, digit product and multiplicative digital root can be used as check values, but are less common. For many digits, they often become 0, because only one 0 is needed to cause this. If without 0 is selected, the Zero as digit is ignored.
The digit product is always smaller than the number from which it is calculated. The digit product has fewer applications than the digit sum, but it does have a few mathematically interesting aspects. The graph of the simple digit product has properties similar to those of a fractal, as its vertices, the local maxima, and its zeros, the local minima, are self-similar. However, it is not a fractal in the traditional sense, as it is defined only for natural numbers.
Also interesting are the multiplicative digital root and the magnitude of persistence. The smallest number with a persistence of 11 is 277777788888899. No number has yet been discovered with a persistence of 12 or higher. This, of course, only applies to calculations involving zero.
