Absolutely! Let’s complete each factor tree to find the
prime factors of 42, 84, 210, and 162.
---
## 🔢 1. Factor Tree for 42
We are given:
- 42 splits into
7 and a blank box.
Since 7 × ? = 42 → ? = 42 ÷ 7 =
6
So the next box is
6.
Now, factor 6:
6 = 2 × 3 → both are prime!
✔ So the completed tree:
```
42
/ \
7 6
/ \
2 3
```
Prime factors of 42: 2, 3, 7
---
## 🔢 2. Factor Tree for 84
Given:
- 84 splits into a blank box and
21
So, ? × 21 = 84 → ? = 84 ÷ 21 =
4
So first box =
4
Now factor 4:
4 = 2 × 2 → both prime.
Factor 21:
21 = 3 × 7 → both prime.
✔ Completed tree:
```
84
/ \
4 21
/ \ / \
2 2 3 7
```
Prime factors of 84: 2, 2, 3, 7 (or 2² × 3 × 7)
---
## 🔢 3. Factor Tree for 210
We need to break down 210.
Let’s pick an easy factor — 210 is even → divisible by
2
210 ÷ 2 =
105
So:
- Left branch:
2
- Right branch:
105
Now factor 105: ends in 5 → divisible by
5
105 ÷ 5 =
21
Then factor 21: 3 × 7
✔ Completed tree:
```
210
/ \
2 105
/ \
5 21
/ \
3 7
```
Prime factors of 210: 2, 3, 5, 7
---
## 🔢 4. Factor Tree for 162
162 is even → divisible by
2
162 ÷ 2 =
81
So:
- Left branch:
2
- Right branch:
81
Now factor 81: 81 = 9 × 9
But 9 is not prime → 9 = 3 × 3
So 81 = 3 × 3 × 3 × 3
We can split 81 as 9 and 9, then each 9 into 3 and 3.
✔ Completed tree:
```
162
/ \
2 81
/ \
9 9
/ \ / \
3 3 3 3
```
Prime factors of 162: 2, 3, 3, 3, 3 (or 2 × 3⁴)
---
##
✔ Final Answers (Filled-in Trees):
➤ 42:
- Top: 42
- Left: 7
- Right: 6 → splits into 2 and 3
➤ 84:
- Top: 84
- Left: 4 → splits into 2 and 2
- Right: 21 → splits into 3 and 7
➤ 210:
- Top: 210
- Left: 2
- Right: 105 → splits into 5 and 21 → 21 splits into 3 and 7
➤ 162:
- Top: 162
- Left: 2
- Right: 81 → splits into 9 and 9 → each 9 splits into 3 and 3
---
## 📌 Prime Factorizations Summary:
-
42 = 2 × 3 × 7
-
84 = 2² × 3 × 7
-
210 = 2 × 3 × 5 × 7
-
162 = 2 × 3⁴
You can now fill in all the blanks on your worksheet with these numbers!
Let me know if you want this drawn out visually or explained step-by-step for a child! 😊
Parent Tip: Review the logic above to help your child master the concept of to do factor trees worksheet.
