Question

If M, A and T are distinct positive integers such that $M 	imes A 	imes T = 1947$, then which of the following is the maximum possible value of $M + A + T$?

Accepted Answer

C. Prime factorization of $1947 = 3 	imes 11 	imes 59$. Since $M, A, T$ are distinct positive integers, we can write $1947$ as a product of three distinct integers: 1. $1 	imes 3 	imes 649 \Rightarrow$ Sum $= 1 + 3 + 649 = 653$ 2. $1 	imes 11 	imes 177 \Rightarrow$ Sum $= 1 + 11 + 177 = 189$ 3. $3 	imes 11 	imes 59 \Rightarrow$ Sum $= 3 + 11 + 59 = 73$ The maximum possible value among these is $653$.

Maximum Value of Sum of Factors

Explanation

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