What times what equals 40?
Understand the Problem
The question is asking for pairs of numbers that, when multiplied together, equal 40. This involves identifying the factors of the number 40.
Answer
(1, 40), (2, 20), (4, 10), (5, 8), (-1, -40), (-2, -20), (-4, -10), (-5, -8)
Answer for screen readers
The pairs of numbers that equal 40 when multiplied are (1, 40), (2, 20), (4, 10), (5, 8), (-1, -40), (-2, -20), (-4, -10), and (-5, -8).
Steps to Solve
- List all factor pairs of 40
Factors of 40 are the integers which, when multiplied together in pairs, yield the product of 40:
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Begin by finding the smallest factor (other than 1) and work upwards to find its corresponding pair.
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For 40: $$1 \times 40 = 40$$ $$2 \times 20 = 40$$ $$4 \times 10 = 40$$ $$5 \times 8 = 40$$
Therefore, the factor pairs are: $$ (1, 40), (2, 20), (4, 10), (5, 8) $$
- Consider negative factors
When considering negative numbers, the products still yield 40. Each of the positive factor pairs will have a corresponding negative pair: $$ -1 \times -40 = 40 $$ $$ -2 \times -20 = 40 $$ $$ -4 \times -10 = 40 $$ $$ -5 \times -8 = 40 $$
Therefore, the negative factor pairs are: $$ (-1, -40), (-2, -20), (-4, -10), (-5, -8) $$
The pairs of numbers that equal 40 when multiplied are (1, 40), (2, 20), (4, 10), (5, 8), (-1, -40), (-2, -20), (-4, -10), and (-5, -8).
More Information
These factor pairs include both positive and negative integers, but their products are the same.
Tips
A common mistake is forgetting to consider negative factor pairs. Since a negative times a negative equals a positive, they should be included.
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