The factors of 252 in pairs are the sets of two numbers that multiply together to give 252.
Understanding Factor Pairs
A factor pair consists of two integers that, when multiplied together, result in a specific product. For any given number, finding its factor pairs involves systematically identifying all integer pairs that divide the number evenly.
All Factor Pairs of 252
Here is a comprehensive list of all factor pairs for the number 252:
| Factor 1 | Factor 2 | Product |
|---|---|---|
| 1 | 252 | 252 |
| 2 | 126 | 252 |
| 3 | 84 | 252 |
| 4 | 63 | 252 |
| 6 | 42 | 252 |
| 7 | 36 | 252 |
| 9 | 28 | 252 |
| 12 | 21 | 252 |
| 14 | 18 | 252 |
Each pair in the table above demonstrates how two numbers multiply to equal 252.
How to Determine Factor Pairs Systematically
One effective way to find all factor pairs of a number like 252 is by using its prime factorization and then systematically combining the prime factors.
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Prime Factorization: First, break down the number into its prime factors.
- 252 = 2 × 126
- 252 = 2 × 2 × 63
- 252 = 2 × 2 × 3 × 21
- 252 = 2 × 2 × 3 × 3 × 7
- Therefore, the prime factorization of 252 is 2² × 3² × 7¹.
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Generate All Factors: Use these prime factors and their exponents to generate all possible individual factors. For each prime factor, consider all powers from zero up to its exponent in the prime factorization.
- For 2²: 2⁰=1, 2¹=2, 2²=4
- For 3²: 3⁰=1, 3¹=3, 3²=9
- For 7¹: 7⁰=1, 7¹=7
- Multiplying these combinations gives all individual factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
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Pair Them Up: Arrange these individual factors in ascending order. Then, pair them from the ends inwards (smallest with largest, second smallest with second largest, and so on) until you reach the middle. This method ensures that all unique factor pairs are identified without missing any.
This systematic approach confirms that the list provided above includes all the factor pairs for 252.
