Question

Rowan has two pieces of cable, one 15 feet long and the other 12 feet long. For a science project he wants to cut them up to produces pieces of cable that are all the same length, with no cable left over. What is the greatest length, in feet, that he can make them?

Answer 1

3 feet

Explanation:

To solve this problem the heed to find the factors of 15 and 12

Factors of both numbers

12 : 1,2,3,4,6,12

15: :1.3,5,15

Then we find the highest common factor between them which is 3, 3 is a factor of both 12 and 15

remainder. The highest common factor is found as follows:

So, if both cables are cut into 3 feet each, you should have a total of 9 piecesa total of 9 pieces of cables.

From the 12 feet long cable you should have 3 feet x 4 meaning 4 pieces

From the 15 fert long cable you should have 3 feet x5 meaning 5 pieces

4+5 makes it 9 pieces without any remainder

Answer 2

The greatest length she can cut to have equal length in all the cables, without a left over is 3 feet each

Explanation:

in order to solve this, we treat the length of each cable as separate numbers for which we find the highest common factor, since we are told that they must all be of the same length. The highest common factor of two whole numbers, is the highest number which completely divides both number without a remainder. The highest common factor is found as follows:

Factors of 12 are : 1, 2, 3, 4, 6, and 12

factors of 15 are : 1, 3, 5, and 15

from the above, the highest factor that is common to both numbers is 3.

Therefore, if both cables are cut into 3 feet each, , a total of 9 pieces of cables (4 from the 12 feet cable and 5 from the 15 feet cable) of equal length will be obtained without any remainder.