Maximum Value of Sum of Factors

Prime factorization of $1947 = 3 \times 11 \times 59$.

Since $M, A, T$ are distinct positive integers, we can write $1947$ as a product of three distinct integers:

1. $1 \times 3 \times 649 \Rightarrow$ Sum $= 1 + 3 + 649 = 653$
2. $1 \times 11 \times 177 \Rightarrow$ Sum $= 1 + 11 + 177 = 189$
3. $3 \times 11 \times 59 \Rightarrow$ Sum $= 3 + 11 + 59 = 73$

The maximum possible value among these is $653$.