Factors Worksheets - Free Printable

To solve the factor tree problems, we need to break down each number into its prime factors. Let's go through each part step by step.

---

Part a:

The number is 30.
- Start with 30 and split it into two factors: \(30 = 2 \times 15\).
- Next, factor 15 into \(15 = 3 \times 5\).
- Both 2, 3, and 5 are prime numbers.

So, the completed factor tree is:
```
30
/ \
2 15
/ \
3 5
```

---

Part b:

The number is 63.
- Start with 63 and split it into two factors: \(63 = 9 \times 7\).
- Next, factor 9 into \(9 = 3 \times 3\).
- Both 3 and 7 are prime numbers.

So, the completed factor tree is:
```
63
/ \
9 7
/ \
3 3
```

---

Part c:

The number is 27.
- Start with 27 and split it into two factors: \(27 = 9 \times 3\).
- Next, factor 9 into \(9 = 3 \times 3\).
- All the factors (3, 3, 3) are prime numbers.

So, the completed factor tree is:
```
27
/ \
9 3
/ \
3 3
```

---

Part d:

The number is 56.
- Start with 56 and split it into two factors: \(56 = 8 \times 7\).
- Next, factor 8 into \(8 = 4 \times 2\).
- Then, factor 4 into \(4 = 2 \times 2\).
- All the factors (2, 2, 2, 7) are prime numbers.

So, the completed factor tree is:
```
56
/ \
8 7
/ \
4 2
/ \
2 2
```

---

Part e:

The number is 100.
- Start with 100 and split it into two factors: \(100 = 10 \times 10\).
- Next, factor each 10 into \(10 = 2 \times 5\).
- So, \(100 = 2 \times 5 \times 2 \times 5\).
- All the factors (2, 2, 5, 5) are prime numbers.

So, the completed factor tree is:
```
100
/ \
10 10
/ \ / \
2 5 2 5
```

---

Final Answers:

- a: \(30 = 2 \times 3 \times 5\)
- b: \(63 = 3 \times 3 \times 7\)
- c: \(27 = 3 \times 3 \times 3\)
- d: \(56 = 2 \times 2 \times 2 \times 7\)
- e: \(100 = 2 \times 2 \times 5 \times 5\)

Boxed Answer:

\[
\boxed{
\text{a: } 2 \times 3 \times 5, \quad
\text{b: } 3 \times 3 \times 7, \quad
\text{c: } 3 \times 3 \times 3, \quad
\text{d: } 2 \times 2 \times 2 \times 7, \quad
\text{e: } 2 \times 2 \times 5 \times 5
}
\]