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?

Answers

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

User avatar for Will Carington

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.

For more help, make sure to check out Noodle's math resources, browse or learning materials database, or even use Noodle to search for a math tutor. Hope this helps, and good luck!

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