What are Factors?
Factors of a number are integers that can multiply together to produce the number without leaving a remainder.
Factors of 32
The factors of 32 are numbers that multiply in pairs to give the original number. Since 32 is an even composite number, its factors include 1, 2, 4, 8, 16, and 32.
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Pair Factors of 32
Pair factors are combinations of numbers that, when multiplied, result in 32. For 32, the positive pairs are (1, 32), (2, 16), and (4, 8), while the negative pairs are (-1, -32), (-2, -16), and (-4, -8).
Division Method to Find Factors
Using the division method, we can determine factors by dividing 32 by integers and checking for a remainder of 0. The factors of 32 obtained through division are 1, 2, 4, 8, 16, and 32.
| Division | Factor | Remainder |
|---|---|---|
| 32 ÷ 1 | 32 | 0 |
| 32 ÷ 2 | 16 | 0 |
| 32 ÷ 4 | 8 | 0 |
| 32 ÷ 8 | 4 | 0 |
| 32 ÷ 16 | 2 | 0 |
| 32 ÷ 32 | 1 | 0 |
Prime Factorization of 32
Prime factorization expresses a number as a product of prime numbers. For 32, the prime factors are all 2s: 32 = 2^5.
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Examples
- Distribution Example: If 32 apples are shared among 8 friends, each gets 4 apples (32 ÷ 8).
- Tent Example: With 32 soldiers and 4 tents, each tent houses 8 soldiers (32 ÷ 4).
- Common Factors: Between 32 and 64, common factors are 1, 2, 4, 8, 16, 32. For 32, 36, and 42, common factors are identified by listing and comparing their factors.
Conclusion
Understanding the factors of 32 involves recognizing its divisible integers, using both pair and division methods. Prime factorization simplifies it further by identifying the prime factors that compose 32.
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