You can multiply several pairs of numbers to get 52. These pairs are known as the factor pairs of 52.
Understanding Factor Pairs of 52
A factor pair consists of two numbers that, when multiplied together, result in a specific product. For the number 52, we are looking for two integers whose product is 52.
The positive factor pairs for the number 52 are:
| Multiplication | Factor Pair |
|---|---|
| 1 x 52 | (1, 52) |
| 2 x 26 | (2, 26) |
| 4 x 13 | (4, 13) |
Each of these pairs represents two numbers that, when multiplied, will equal 52. For instance, if you multiply 4 by 13, the result is 52. Similarly, multiplying 1 by 52 or 2 by 26 also yields 52.
How to Find Factor Pairs
To find the factor pairs of any number, you typically start by dividing the number by consecutive integers starting from 1. If the division results in a whole number (no remainder), then both the divisor and the quotient form a factor pair.
- Step 1: Divide 52 by 1. The result is 52. So, (1, 52) is a factor pair.
- Step 2: Divide 52 by 2. The result is 26. So, (2, 26) is a factor pair.
- Step 3: Divide 52 by 3. The result is 17.33 (not a whole number).
- Step 4: Divide 52 by 4. The result is 13. So, (4, 13) is a factor pair.
- Step 5: Continue this process. The next number to check would be 5, then 6, and so on, until the divisor exceeds the square root of 52 (which is approximately 7.2). Since we already found 13, and 13 is greater than 7.2, we've found all the unique positive integer factor pairs.
It's also worth noting that negative numbers can form factor pairs. For example, (-1) x (-52) = 52, (-2) x (-26) = 52, and (-4) x (-13) = 52. However, when discussing "factor pairs" in a general context, positive integers are most commonly implied.
