# Let A =1, B=2, C=3,..., Z= 26. The product value of a word is equal to the product of the values of its letters. For example, BAD has a product value of 2*1*4=8. What common English word has a product value of 715?

##### Anonymous, The Answer is: make

Prime factorize 715 to find 715=5 x 11 x 13. The only ways to write 715 as a product of positive integers greater than 1 are the distinct ways of grouping the prime factors:

(5) x (11) x (13) = 5 x 11 x 13

(5 x 11) x 13=55 x 13

5 x (11 x 13)=5 x 143

(5 x 13) x 11=65 x 11 and

(5 x 11 x 13)=715

where the last one is a product with only one factor. Since the letters cannot represent numbers greater than 26, only 5 x 11 x 13 could come from calculating the product value of a word. The 5th, 11th, and 13th letters of the alphabet are E, K, and M. Since E, K, and M do not form a word, we introduce the letter A (which doesn't affect the product since its value is 1) to form the word MAKE

##### Anonymous, Answer of question I think

So we are just supposed to find factors of 715 to get the answer?

##### Will Carington, works for Noodle This question is essentially asking "What series of numbers between 1 and 26 (which represent the letters A-Z) can you multiply in order to get 715?" To find out, try finding the factors of 715.

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