For Questions 182: List all factor pairs for the following number (Pairs of Integers which multiply to give the number) You can earn: 1 point for getting 2 or more pairs 1 point for getting all of the pairs square 40 40 square 60 60

To find all factor pairs for a given number, we need to identify pairs of integers that multiply together to give the original number.<br /><br />**Factor Pairs for 40:**<br /><br />1. Start with 1 and the number itself:<br /> - \(1 \times 40 = 40\)<br /> - Factor pair: (1, 40)<br /><br />2. Check the next integer, 2:<br /> - \(2 \times 20 = 40\)<br /> - Factor pair: (2, 20)<br /><br />3. Check the next integer, 3:<br /> - 40 is not divisible by 3, so no factor pair here.<br /><br />4. Check the next integer, 4:<br /> - \(4 \times 10 = 40\)<br /> - Factor pair: (4, 10)<br /><br />5. Check the next integer, 5:<br /> - \(5 \times 8 = 40\)<br /> - Factor pair: (5, 8)<br /><br />6. Check the next integer, 6:<br /> - 40 is not divisible by 6, so no factor pair here.<br /><br />7. Check the next integer, 7:<br /> - 40 is not divisible by 7, so no factor pair here.<br /><br />Since we've reached the square root of 40 (approximately 6.32), we can stop checking further.<br /><br />The complete list of factor pairs for 40 is: <br />(1, 40), (2, 20), (4, 10), (5, 8)<br /><br />**Factor Pairs for 60:**<br /><br />1. Start with 1 and the number itself:<br /> - \(1 \times 60 = 60\)<br /> - Factor pair: (1, 60)<br /><br />2. Check the next integer, 2:<br /> - \(2 \times 30 = 60\)<br /> - Factor pair: (2, 30)<br /><br />3. Check the next integer, 3:<br /> - \(3 \times 20 = 60\)<br /> - Factor pair: (3, 20)<br /><br />4. Check the next integer, 4:<br /> - \(4 \times 15 = 60\)<br /> - Factor pair: (4, 15)<br /><br />5. Check the next integer, 5:<br /> - \(5 \times 12 = 60\)<br /> - Factor pair: (5, 12)<br /><br />6. Check the next integer, 6:<br /> - \(6 \times 10 = 60\)<br /> - Factor pair: (6, 10)<br /><br />7. Check the next integer, 7:<br /> - 60 is not divisible by 7, so no factor pair here.<br /><br />Since we've reached the square root of 60 (approximately 7.75), we can stop checking further.<br /><br />The complete list of factor pairs for 60 is: <br />(1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)