I am having solving the following problem:
If the product of the integer $w,x,y,z$ is 770. and if $1
what is the value of $w+z$ ? (ans=$13$)
Any suggestions on how I could solve this problem ?
I am having solving the following problem:
If the product of the integer $w,x,y,z$ is 770. and if $1
what is the value of $w+z$ ? (ans=$13$)
Any suggestions on how I could solve this problem ?
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
Hint: $770$ is the product of four distinct primes. Why must $w$, $x$, $y$, $z$ each be one of those primes?
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.
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.