I’m about 2 years too late but I’d like to take a crack at this for future reference. The reason 10^7 is used is because 10^7=10,000,000 kbps which is the same things as 10Gbps. When this formula was developed into what it is today, 10gbps was insanely, insanely fast and was decided to be used as the number utilized to calculate the weight of the minimum bandwidth number in the EIGRP formula.
The reason that we are adding weight to each number in EIGRP is easy to understand. EIGRP is a complex formula with different sets of numbers that have varying levels of relevance. We decide how much weight, or relevance, the minimum bandwidth has by taking 10^7 (dividend) and dividing it by the minimum bandwidth (divisor), the resulting number (quotient) multiplied by 256 [Read: 2^8 ‘binary octet max value’] is your weighted bandwidth.
“The multiplication of 256 is done so EIGRP is compatible with IGRP (the predecessor of EIGRP).”