Multiplicative partition
Multiplicative partition (Number theory)
In number theory, a multiplicative partition of an integer n greater than 1 is a way of writing n as a product of integers greater than 1. The number n is itself considered one of these products.
Examples
- 2*2*5, 2*10, 4*5, and 20 are the four multiplicative partitions of 20.
- 3*3*3*3, 3*3*9, 3*27, 9*9, and 81 are the five multiplicative permutations of 81 = 3^4. Because 81 is the fourth power of a prime, 81 has the same number (five) of multiplicative partitions as the number four has of additive partitions.
- 30 = 2*3*5 = 2*15 = 6*5 = 3*10 = 30 has five partitions.