Answer:
There are 192 window panes in total.
Step-by-step explanation:
Since each window has four window panes across and four window panes down,the number of panes per window is:
The total number of window panes in 'n' windows is:
With n = 12 windows, the expression that describes the total number of window panes is:
There are 192 window panes in total.
Let's try to find some primes that divide this number.
The number is not divisible by 2, because it is odd.
The number is divisible by 3 though, because the sum of its digits is:
So, we can divide the number by 3 and keep going with the factorization:
This number is again divisible by 3, because
We have
This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have
And 557 is prime, so we're done. This means that the prime factorization of 65169 is