Factors of 32
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.
Also Check: Factors of 215
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.
Also Check: Factors of 144
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.
Also Check: Factors of 150
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Frequently Asked Questions on Factors of 32
The sum of all factors of 32 is calculated by adding 1, 2, 4, 8, 16, and 32, resulting in 63.
The prime factorization of 32 is 2^5.
The positive pair factors of 32 are (1, 32), (2, 16), and (4, 8).
The negative pair factors of 32 are (-1, -32), (-2, -16), and (-4, -8).
Yes, 1 is a factor of 32 because it divides 32 leaving a remainder of 0.