What times what equals 196?
Understand the Problem
The question is asking to find two numbers that, when multiplied together, result in 196. This involves identifying factor pairs of the number 196.
Answer
The factor pairs of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).
Answer for screen readers
The factor pairs of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).
Steps to Solve
- Finding Factor Pairs
To solve the problem, start by determining the factor pairs of 196. A factor pair consists of two numbers that multiply together to give 196.
- Starting with 1 and 196
The first factor pair we can identify is (1, 196) because $1 \times 196 = 196$.
- Continuing with other numbers
Next, we can test integers sequentially up to the square root of 196 (which is about 14) to find other factor pairs:
- 2 is a factor since $2 \times 98 = 196$, so we have the pair (2, 98).
- 4 is also a factor since $4 \times 49 = 196$, so we have (4, 49).
- 7 is a factor as $7 \times 28 = 196$, giving us (7, 28).
- Finally, $14 \times 14 = 196$, yielding the pair (14, 14).
- Listing all factor pairs
Now we have the complete set of factor pairs for 196:
- (1, 196)
- (2, 98)
- (4, 49)
- (7, 28)
- (14, 14)
The factor pairs of 196 are (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14).
More Information
Factor pairs of a number are crucial for understanding multiplication and division. They help break down products into simpler components, which is useful in factoring polynomials and understanding properties of numbers.
Tips
- Failing to check all numbers up to the square root of 196. Always test up to it, as larger factors will repeat the pairs found with smaller factors.
- Not recognizing that the order of factor pairs does not matter (e.g., (2, 98) is the same as (98, 2)).
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