Riley is packing 144 pencils, 120 files, and 108 notebooks into as many boxes as possible. find the greatest number of boxes that riley could pack the items into.

Greatest number of boxes to pack all items into them equally will be 12 where each box contain 10,12,9 files, notebooks and pencils respectively.

Step-by-step explanation:

To find the greatest number of boxes that Riley could pack the items into, we have to find the HCF of 144, 120 and 108.

We will find the HCF through prime factorization.

("Prime Factorization" is finding which prime numbers multiply together to make the original number)

Step 1:

Find the prime factorization of each of the given numbers.

Step 2:

The product of all common prime factors is the HCF of the given numbers.

First number is 120:

120 = 2*2*2*3*5

Second number is 144:

144 = 2*2*2*2*3*3

And last number is 108:

108 = 2*2*3*3*3

Now we will match the numbers which are common in all three values. In other words we will find the common factors.

The common factors in 120,108 and 144 are:

2*2*3

If we multiply 2*2*3 we get 12

Hence, HCF of ( 120,108,144 ) = 12

Therefore, Greatest number of boxes to pack all items into them equally will be 12 where each box contain 10,12,9 files, notebooks and pencils respectively.

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)