When dealing with numbers, understanding their factors can help solve problems related to divisibility, prime factorization, and arithmetic operations. In this article, we’ll focus on finding all the factors of 34,815 and explain the step-by-step process to help you understand how to determine these factors.
What Are Factors?
Before diving into the factors of 34,815, let’s clarify what factors are. A factor of a number is a whole number that divides that number without leaving a remainder. For example, 2 and 5 are factors of 10 because both divide 10 exactly, resulting in whole numbers (5 and 2, respectively).
How to Find the Factors of 34,815
To find the factors of 34,815, we need to identify all the numbers that divide 34,815 without leaving a remainder.
Step 1: Start with the Smallest Prime Number
We begin by dividing 34,815 by the smallest prime number, which is 2. Since 34,815 is an odd number, it is not divisible by 2. Next, we try the next smallest prime number, which is 3.
34,815 divided by 3 equals 11,605, which is a whole number, indicating that 3 is a factor of 34,815. We continue this process with 11,605.
Step 2: Continue with Prime Factorization
We repeat the division by 3:
11,605 ÷ 3 = 3,868.33 (Not a whole number)
Since 11,605 is not divisible by 3, we move to the next prime number, 5:
11,605 ÷ 5 = 2,321 (a whole number)
Since 2,321 is a whole number, 5 is a factor of 11,605. We continue this process with 2,321.
Next, we check for divisibility by 7, the next prime number:
2,321 ÷ 7 = 331.57 (Not a whole number)
Next, we check for divisibility by 11:
2,321 ÷ 11 = 211 (a whole number)
We continue dividing by smaller prime numbers until all factors are obtained.
Step 3: List All Factors
Once we complete the division process, we get the following prime factors of 34,815:
3, 5, 11, and 211.
Therefore, the prime factorization of 34,815 is:
34,815 = 3 × 5 × 11 × 211
Now, to find all factors, we generate combinations of these prime numbers, including their powers:
- 1 (since 1 is a factor of every number)
- 3, 5, 11, 211
- 3 × 5 = 15
- 3 × 11 = 33
- 3 × 211 = 633
- 5 × 11 = 55
- 5 × 211 = 1055
- 11 × 211 = 2321
- 3 × 5 × 11 = 165
- 3 × 5 × 211 = 3165
- 3 × 11 × 211 = 6963
- 5 × 11 × 211 = 11605
- 3 × 5 × 11 × 211 = 34815
Thus, the complete list of factors of 34,815 is:
1, 3, 5, 11, 15, 33, 55, 165, 211, 633, 1055, 2321, 3165, 6963, 11605, and 34815
Table of the factors of 34,815:
| Factor | Pair Factor |
|---|---|
| 1 | 34815 |
| 3 | 11605 |
| 5 | 6963 |
| 11 | 3165 |
| 15 | 2321 |
| 33 | 1055 |
| 55 | 633 |
| 165 | 211 |
| 211 | 165 |
| 633 | 55 |
| 1055 | 33 |
| 2321 | 15 |
| 3165 | 11 |
| 6963 | 5 |
| 11605 | 3 |
| 34815 | 1 |
Step 6: Verify with a Factor Calculator
To quickly find factors without manual calculation, use our Free Factor Calculator. Simply enter 34815 into the calculator, and it will instantly display all its factors.
Conclusion
The factors of 34,815 are 1, 3, 5, 11, 15, 33, 55, 165, 211, 633, 1055, 2321, and 34815. By understanding the step-by-step method of prime factorization, you can find the factors of any number. Whether you are solving a math problem or exploring number properties, this technique will always come in handy.
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