Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having solving the following problem:

If the product of the integer $w,x,y,z$ is 770. and if $1<w<x<y<z$ what is the value of $w+z$ ? (ans=$13$)

Any suggestions on how I could solve this problem ?

share|improve this question
add comment

4 Answers 4

up vote 2 down vote accepted

The number 770 is the product of the prime numbers 2,5,7,11 , and 1<2<5<7<11 Thus, the answer is 2+11 = 13 . Hope this helps

share|improve this answer
1  
What do you mean by the word "u"??? –  The Chaz 2.0 Sep 17 '12 at 11:24
add comment

Hint: $770$ is the product of four distinct primes. Why must $w$, $x$, $y$, $z$ each be one of those primes?

share|improve this answer
add comment

I would proceed as follows. As you know that $$w \cdot x\cdot y\cdot z = 770$$ and $1 < w$, we can start with supposing that $w=2$. After dividing both sides of original equation by $w$, we are left with $$ x \cdot y \cdot z = 385.$$ Now, 3 does not divide 385, so it cannot be the next integer I try for $x$. However, we can find an integer not much larger than 3. Continue in this manner until you have found all of the integers.

share|improve this answer
add comment

Find the prime factorization of the number. That is always a great place to start when you have a problem involving a product of integer. Now here you are lucky, you find $4$ prime numbers to the power of one, so you know your answer is unique.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.