Write three different factors of 224 with a sum between 99 and 110

To find three factors of 224 whose sum is between 99 and 110, we can start by determining the factors of 224.

### Factors of 224:
- \(1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224\)

Next, we need to choose three factors that add up to a value between 99 and 110.

Let’s try the following combinations:

1. **112, 4, and 8**:
   \[
   112 + 4 + 8 = 124 \quad \text{(too high)}
   \]

2. **56, 32, and 8**:
   \[
   56 + 32 + 8 = 96 \quad \text{(too low)}
   \]

3. **56, 28, and 16**:
   \[
   56 + 28 + 16 = 100 \quad \text{(this works, sum = 100)}
   \]

So, the three factors of 224 are **56, 28, and 16**, and their sum is 100, which is between 99 and 110.

Would you like more details or have any questions?

### 5 Related Questions:
1. What is the prime factorization of 224?
2. Can you find more sets of three factors of 224 with sums between 99 and 110?
3. How do you determine if a number is a factor of another number?
4. Can the factors of 224 be expressed as products of smaller numbers?
5. What is the greatest common divisor (GCD) of 224 and another number?

### Tip:
When factoring a number, always start by identifying its prime factors, which can simplify the process of finding all possible factors.

Explore how to find three factors of 224 whose sum falls between 99 and 110. Using basic number theory and factorization, this problem provides a step-by-step solution for middle school students (Grades 6-8), explaining how factors like 56, 28, and 16 add up to 100.

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