Factors of numbers from 66 to 100 | 4th grade Math Worksheet ... - Free Printable

Problem Description:

The task involves finding the factors of specific numbers between 66 and 100. The goal is to list all the factors of each number in the provided boxes and then circle the factors of certain numbers as instructed.

Steps to Solve:

#### Step 1: Understand the Task
- We need to find all the factors of the given numbers.
- A factor of a number is any integer that divides the number evenly (i.e., leaves no remainder).
- After listing the factors, we will circle the factors of specific numbers as indicated.

#### Step 2: List the Factors of Each Number
We will systematically list the factors of each number from 66 to 100.

---

#### Number 66:
Factors of 66:
- Start with 1 and 66: \(1 \times 66 = 66\)
- Check 2: \(2 \times 33 = 66\)
- Check 3: \(3 \times 22 = 66\)
- Check 4: Not a factor
- Check 5: Not a factor
- Check 6: \(6 \times 11 = 66\)
- Stop at \(\sqrt{66} \approx 8.1\), since factors repeat after this point.

Thus, the factors of 66 are:
1, 2, 3, 6, 11, 22, 33, 66

---

#### Number 72:
Factors of 72:
- Start with 1 and 72: \(1 \times 72 = 72\)
- Check 2: \(2 \times 36 = 72\)
- Check 3: \(3 \times 24 = 72\)
- Check 4: \(4 \times 18 = 72\)
- Check 6: \(6 \times 12 = 72\)
- Check 8: \(8 \times 9 = 72\)
- Stop at \(\sqrt{72} \approx 8.5\).

Thus, the factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

---

#### Number 75:
Factors of 75:
- Start with 1 and 75: \(1 \times 75 = 75\)
- Check 3: \(3 \times 25 = 75\)
- Check 5: \(5 \times 15 = 75\)
- Stop at \(\sqrt{75} \approx 8.7\).

Thus, the factors of 75 are:
1, 3, 5, 15, 25, 75

---

#### Number 78:
Factors of 78:
- Start with 1 and 78: \(1 \times 78 = 78\)
- Check 2: \(2 \times 39 = 78\)
- Check 3: \(3 \times 26 = 78\)
- Check 6: \(6 \times 13 = 78\)
- Stop at \(\sqrt{78} \approx 8.8\).

Thus, the factors of 78 are:
1, 2, 3, 6, 13, 26, 39, 78

---

#### Number 82:
Factors of 82:
- Start with 1 and 82: \(1 \times 82 = 82\)
- Check 2: \(2 \times 41 = 82\)
- Stop at \(\sqrt{82} \approx 9.1\).

Thus, the factors of 82 are:
1, 2, 41, 82

---

#### Step 3: Circle the Specified Factors
The task asks us to circle the factors of specific numbers:
1. Circle the factors of 78:
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
Circle these in the box for 78.

2. Circle the factors of 75:
Factors of 75: 1, 3, 5, 15, 25, 75
Circle these in the box for 75.

3. Circle the factors of 82:
Factors of 82: 1, 2, 41, 82
Circle these in the box for 82.

---

#### Final Answer:
- Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 75: 1, 3, 5, 15, 25, 75
- Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
- Factors of 82: 1, 2, 41, 82

Circled Factors:
- For 78: 1, 2, 3, 6, 13, 26, 39, 78
- For 75: 1, 3, 5, 15, 25, 75
- For 82: 1, 2, 41, 82

$$
\boxed{\text{See the detailed steps above for the solution.}}
$$