Prime Factor Trees (Range 4 to 48) (A) - Free Printable

Let’s solve each factor tree step by step. We’ll break down each number into its prime factors using the given structure.

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1. Factor Tree for 70

We are told that 70 splits into 7 and a blank square.

→ 70 ÷ 7 = 10 → so the square is 10

Now, 10 splits into two circles (prime factors).

→ 10 = 2 × 5 → both are prime.

So:
- Square under 70: 10
- Circles under 10: 2 and 5

Prime factors of 70: 2, 5, 7

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2. Factor Tree for 210

Given: 210 splits into a blank square and 6.

→ 210 ÷ 6 = 35 → so the left square is 35

Now, 35 splits into two circles (primes):

→ 35 = 5 × 7 → both prime.

Also, 6 splits into two circles:

→ 6 = 2 × 3 → both prime.

So:
- Left square: 35
- Circles under 35: 5, 7
- Circles under 6: 2, 3

Prime factors of 210: 2, 3, 5, 7

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3. Factor Tree for 132

Starts with 132 splitting into a circle and a square.

Let’s pick an easy prime factor — 132 is even → divisible by 2.

→ 132 ÷ 2 = 66 → so circle = 2, square = 66

Now, 66 splits into a circle and a square.

66 is also even → 66 ÷ 2 = 33 → circle = 2, square = 33

Now, 33 splits into two circles.

→ 33 = 3 × 11 → both prime.

So:
- First circle (under 132): 2
- First square: 66
- Second circle (under 66): 2
- Second square: 33
- Last two circles: 3, 11

Prime factors of 132: 2, 2, 3, 11

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4. Factor Tree for 300

300 splits into two squares.

Let’s try dividing by small primes.

Option: 300 = 10 × 30 → but let’s use smaller steps to match tree structure.

Better: 300 = 3 × 100? Or 2 × 150? Let’s go with 300 = 10 × 30? But we need to fit the tree.

Looking at the tree: top splits into two squares. Then left square splits into two circles. Right square splits into one circle and one square, which then splits into two circles.

Try:

300 = 10 × 30 → but 10 and 30 aren’t prime.

Wait — better to start with prime factors.

But since the tree has specific branches, let’s follow it logically.

Assume:

Left branch: 300 → square A and square B

Suppose square A = 10 → then 300 ÷ 10 = 30 → square B = 30

Then square A (10) → splits into two circles: 2 and 5 → good.

Square B (30) → splits into one circle and one square.

30 = 3 × 10 → so circle = 3, square = 10

Then that square (10) → splits into 2 and 5.

Perfect! That fits the tree shape.

Check:

Top: 300 → 10 and 30

Left: 10 → 2, 5

Right: 30 → 3 and 10 → then 10 → 2, 5

So all leaves: 2, 5, 3, 2, 5 → wait, that’s five numbers? But 300 = 2² × 3 × 5² → yes, five prime factors counting multiplicity.

In the tree:

- Left square: 10
- Right square: 30
- Under left square (10): circles 2, 5
- Under right square (30): circle 3, square 10
- Under that last square (10): circles 2, 5

Yes, matches.

Alternative path: could do 300 = 15 × 20? But doesn’t fit as cleanly.

Our choice works.

So:

- Top-left square: 10
- Top-right square: 30
- Under 10: 2, 5
- Under 30: 3, 10
- Under bottom 10: 2, 5

Prime factors: 2, 2, 3, 5, 5

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Now, let’s write the final answers in order for each tree.

Final Answer:

For 70:
Square: 10
Circles: 2, 5

For 210:
Left square: 35
Circles under 35: 5, 7
Circles under 6: 2, 3

For 132:
First circle: 2
First square: 66
Second circle: 2
Second square: 33
Last circles: 3, 11

For 300:
Top-left square: 10
Top-right square: 30
Under 10: 2, 5
Under 30: 3, 10
Under bottom 10: 2, 5

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Final Answer:
70 → [10] → [2, 5]
210 → [35, 6] → [5, 7], [2, 3]
132 → [2, 66] → [2, 33] → [3, 11]
300 → [10, 30] → [2, 5], [3, 10] → [2, 5]