Need help . A board is 24 inches long. Find all the whole- number lengths into which it can be evenly divided
Factors of 24:
1, 24
2, 12
3, 8
4, 6
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To find all the whole-number lengths into which a 24-inch board can be evenly divided, we need to determine the factors of 24. Factors are the numbers that divide evenly into a given number without leaving a remainder.
One way to find the factors of 24 is to start with the number 1 and check if it divides evenly into 24. If it does, then it is a factor. We continue this process up to the square root of 24, as any factors beyond that point would be repetitive.
Let's go through this step-by-step:
1. Start with the number 1.
- 24 ÷ 1 = 24 (no remainder), so 1 is a factor.
2. Move to the next number, 2.
- 24 ÷ 2 = 12 (no remainder), so 2 is a factor.
3. Move to the next number, 3.
- 24 ÷ 3 = 8 (no remainder), so 3 is a factor.
4. Move to the next number, 4.
- 24 ÷ 4 = 6 (no remainder), so 4 is a factor.
5. Continue this process until the square root of 24, which is approximately 4.9. We can round up to 5, as we only need whole-number factors.
- 24 ÷ 5 = 4.8 (remainder), so 5 is not a factor.
6. Since we've reached the square root of 24, we don't need to check any further.
The whole-number lengths into which a 24-inch board can be evenly divided are: 1, 2, 3, 4, 6, 8, 12, and 24.