Factoring can separate wholes into separate parts with no remainders {factoring and neurons}. Neuron-series-array arrays can check factors to make regions consistent and complete.
factorable
Dividing factorable numbers by correct factors leaves no remainder and results in one dividend, with no addition. For example, 15 is factorable, because 3 * 5 = 15, and 3 and 5 are unique and prime. Dividing factorable polynomials by correct factors leaves no remainder.
remainder
Dividing factorable numbers by incorrect factors leaves incorrect-factor fractions (remainder) that add to dividend. For example, 10/3 = 3 + 1/3. Dividing factorable polynomials by incorrect factors leaves remainders.
logarithms
Dividing factorable numbers by all correct prime factors equals one. For example, 8 has three factors 2, 2, and 2, and 8/(2*2*2) = 2^3 / 2^3 = 1. Logarithm of 1 is 0. For example, log(2^3) / log(2) = log(2^2), log(2^2) / log(2) = log(2^1), log(2^1) / log(2) = log(1) = 0. Alternatively, log(2^3) = 3 and log(2) = 1, so 3 - 1 - 1 - 1 = 0.
Dividing factorable numbers by incorrect factors does not equal one. For example, dividing 8 by 3 makes 2 + 2/3. Logarithm is not zero. For example, log(8) - log(3) is not zero.
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Date Modified: 2022.0224