To find the prime factors using factor trees, we break each number down into two factors, and then break those factors down further until we are left only with prime numbers (numbers that can only be divided by 1 and themselves, like 2, 3, 5, 7).
Here is the step-by-step solution for each number on the worksheet:
1. Number 28
* The tree starts with
28. One branch is given as
7.
* To find the other branch, we divide 28 by 7: $28 \div 7 = 4$. So, the first empty square is
4.
* Now we break down
4. The prime factors of 4 are
2 and
2 ($2 \times 2 = 4$).
*
Prime factors: 2, 2, 7.
2. Number 54
* The tree starts with
54. One branch is given as
9.
* To find the other branch, we divide 54 by 9: $54 \div 9 = 6$. So, the first empty square is
6.
* Now we break down the branches:
* Break down
6: The factors are
2 and
3.
* Break down
9: The factors are
3 and
3.
*
Prime factors: 2, 3, 3, 3.
3. Number 140
* The tree starts with
140. Let's split it into easy numbers, like
10 and
14 ($10 \times 14 = 140$). Let's put
10 in the circle and
14 in the square.
* Break down
10: The factors are
2 and
5.
* Break down
14: The factors are
2 and
7.
*
Prime factors: 2, 2, 5, 7.
4. Number 108
* The tree starts with
108. Let's split it into
12 and
9 ($12 \times 9 = 108$).
* Break down the left side (
12): Split into
3 and
4. Then split
4 into
2 and
2.
* Break down the right side (
9): Split into
3 and
3.
*
Prime factors: 2, 2, 3, 3, 3.
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Final Answer:
1. Factor Tree for 28:
* Top branches: 7 and
4
* Bottom circles (from 4):
2 and
2
* Prime Factors: $2 \times 2 \times 7$
2. Factor Tree for 54:
* Top branches:
6 and 9
* Bottom circles (from 6):
2 and
3
* Bottom circles (from 9):
3 and
3
* Prime Factors: $2 \times 3 \times 3 \times 3$
3. Factor Tree for 140:
* Top branches:
10 and
14 (or vice versa)
* From 10:
2 and
5
* From 14:
2 and
7
* Prime Factors: $2 \times 2 \times 5 \times 7$
4. Factor Tree for 108:
* Top branches:
12 and
9 (or vice versa)
* From 12:
3 and
4 $\rightarrow$ from 4:
2 and
2
* From 9:
3 and
3
* Prime Factors: $2 \times 2 \times 3 \times 3 \times 3$
Parent Tip: Review the logic above to help your child master the concept of to do factor trees worksheet.
