To determine the factors of a number is to find pairs of numbers that, when multiplied together, yield the original number. Let's examine the specific example given, with the number 36.
### Step-by-Step Solution
1. Identify the number:
- The number we're working with is 36.
2. Initialize an empty list of factor pairs:
- Start with an empty list to store pairs of factors.
3. Iterate from 1 to the square root of the number:
- We need to examine each integer from 1 up to the square root of 36, because any factor larger than the square root will have a corresponding factor smaller than the square root. This ensures we don't duplicate factor pairs.
- The square root of 36 is 6.
4. Check for each integer if it’s a factor:
- For i = 1:
- Check if 36 is divisible by 1: 36 ÷ 1 = 36. Since 1 evenly divides 36, (1, 36) is a factor pair.
- Add the pair (1, 36) to the list.
- For i = 2:
- Check if 36 is divisible by 2: 36 ÷ 2 = 18. Since 2 evenly divides 36, (2, 18) is a factor pair.
- Add the pair (2, 18) to the list.
- For i = 3:
- Check if 36 is divisible by 3: 36 ÷ 3 = 12. Since 3 evenly divides 36, (3, 12) is a factor pair.
- Add the pair (3, 12) to the list.
- For i = 4:
- Check if 36 is divisible by 4: 36 ÷ 4 = 9. Since 4 evenly divides 36, (4, 9) is a factor pair.
- Add the pair (4, 9) to the list.
- For i = 5:
- Check if 36 is divisible by 5: 36 ÷ 5 = 7.2. Since 36 is not evenly divisible by 5 (the quotient is not an integer), we do not add (5, 7.2).
- For i = 6:
- Check if 36 is divisible by 6: 36 ÷ 6 = 6. Since 6 evenly divides 36, (6, 6) is a factor pair.
- Add the pair (6, 6) to the list. Note that it’s only added once since both numbers are the same.
5. Compile the list of all factor pairs:
- After iterating through all relevant integers, our list of factor pairs is:
- (1, 36)
- (2, 18)
- (3, 12)
- (4, 9)
- (6, 6)
### Final Result
The factor pairs of 36 are:
- (1, 36)
- (2, 18)
- (3, 12)
- (4, 9)
- (6, 6)
These pairs represent all combinations of numbers that multiply together to give the product 36.
