To find what number times another number equals 80, we are looking for pairs of numbers that, when multiplied together, result in 80. These pairs are commonly referred to as factors of 80.
Understanding Factors of 80
A factor of a number is an integer that divides the number without leaving a remainder. When we ask "what number times another number equals 80?", we are typically interested in the integer pairs that satisfy this condition, though it's important to remember that non-integer solutions also exist.
Positive Integer Factor Pairs of 80
The positive integer pairs that multiply to 80 are:
| First Number | Second Number | Pair |
|---|---|---|
| 1 | 80 | (1, 80) |
| 2 | 40 | (2, 40) |
| 4 | 20 | (4, 20) |
| 5 | 16 | (5, 16) |
| 8 | 10 | (8, 10) |
It's important to remember that multiplication is commutative, meaning the order of the numbers does not change the product. Therefore, if 2 times 40 equals 80, then 40 times 2 also equals 80. The full set of positive integer pairs (considering order) includes:
- 1 × 80 = 80
- 2 × 40 = 80
- 4 × 20 = 80
- 5 × 16 = 80
- 8 × 10 = 80
- 10 × 8 = 80
- 16 × 5 = 80
- 20 × 4 = 80
- 40 × 2 = 80
- 80 × 1 = 80
Negative Integer Factor Pairs of 80
When two negative numbers are multiplied, the product is positive. This means that for every positive integer pair that multiplies to 80, there is a corresponding negative integer pair that also multiplies to 80:
- (-1) × (-80) = 80
- (-2) × (-40) = 80
- (-4) × (-20) = 80
- (-5) × (-16) = 80
- (-8) × (-10) = 80
Similarly, their commutative counterparts (e.g., (-80) × (-1) = 80) also apply.
Beyond Integer Factors
While integer factor pairs are the most common answer to this type of question, it's worth noting that an infinite number of non-integer pairs can also multiply to 80. For example:
- 0.5 × 160 = 80
- 1.25 × 64 = 80
- (1/2) × 160 = 80
In general, for any non-zero real number 'x', the number 'x' multiplied by (80/x) will always equal 80.
