the question is, find a pair of numbers that have the greatest common factor. Tell how you found the pair. 4,6,9,15 are the numbers

## find a pair if numbers that have the given greatest common factor. Tell how you found the pair? the numbers are 4,6,9,15

# 2 Answers

So the problem has given you a list of numbers: 4, 6, 9, and 15 and you are to find the greatest common factor. First we know that a factor is found when something is multiplied. So the first thing we need to do is find what numbers can be multiplied to find the given list of numbers.

I'll start with 4. 1 x 4=4 and 2 x 2 = 4 so the factors here are 1,4, and 2.

Next, is 6. 1 x 6 and 2 x 3. The factors here are 1, 2, 3, and 6.

Then 9. 1 x 9 and 3 x 3. The factors here are 1, 3, and 9

Finally, 15. 1 x 15 and 3 x 5. The factors here are 1, 3, 5, and 15.

Now we go back to the factors we've found and find the largest that all of them have, 1 in this case.

The given numbers can be factorized to get which numbers would have highest common factors:

4= 2^{2 }, 6=2x3, 9=3^{2}, 15=3x5;

now we look for numbers that have common factors like

(4,6) has common factor 2

(6,9) has common factor 3

(6,15) has common factor 3

(9,15) has common factor 3

(4,9), (4,15) has no common factor

As we can see here three pairs (6,9), (6,15) and (9,15) has greatest common factor; which is 3. Since we are asked to find pairs of numbers among the given numbers. The possible pairs are (6,9), (6,15) and (9,15).

Good luck