# The product of two whole numbers is 360 and their sum is less than 100. What are the two possiblities for the two numbers.

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We want two numbers `p,q in ZZ` (whole numbers) whose product is 360 and whose sum is less than 100.

You can use trial and error to list the possible factors:

1,360 sum>100

2,180 sum>100

3,120 sum>100

4,90 works

5,72 works

6,60 works

8,45 works

9,40 works

10,36 works

12,30 works

15,24 works

18,20 works

If you allow negative numbers then all of the above pairs ,negated, will work.

**Sources:**

it can be 6 and 60.

or 90 and 4.