Factors Worksheets - Free Printable

Let's solve the problem step by step.

---

Task:

Place the numbers in the correct positions on the Venn diagrams based on factors of given numbers. We are given pairs of numbers and their factors, and we need to:
- Identify common factors (intersection).
- Place unique factors in the non-overlapping parts.
- Label the sections appropriately.

We’ll go through each Venn diagram one by one.

---

1. Factors of 21 and Factors of 24

Given factors:
- Factors of 21: 1, 3, 7, 21
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Step 1: Find common factors
- Common factors: Numbers that appear in both lists → 1, 3

Step 2: Unique factors
- Only in 21: 7, 21
- Only in 24: 2, 4, 6, 8, 12, 24

Venn Diagram:
- Left circle (Factors of 21): 7, 21
- Intersection: 1, 3
- Right circle (Factors of 24): 2, 4, 6, 8, 12, 24

---

2. Factors of 16 and Factors of 20

Given factors:
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 20: 1, 2, 4, 5, 10, 20

Common factors: 1, 2, 4
Only in 16: 8, 16
Only in 20: 5, 10, 20

Venn Diagram:
- Left (16): 8, 16
- Intersection: 1, 2, 4
- Right (20): 5, 10, 20

---

3. Factors of 49 and Factors of 49? Wait...

Wait — it says:

> Factors of 49
> Factors of 49

That’s a typo or mistake? Let's check.

Actually, looking at the image text:
> Factors of 49
> Factors of 49

But the list below is: 1, 3, 7, 21, 49

Wait — that can’t be right. Let's double-check.

Factors of 49: 1, 7, 49
But the list shows: 1, 3, 7, 21, 49

That suggests it might be Factors of 49 and Factors of 21?

Wait — no, the heading says:
> Factors of 49
> Factors of 49

But the number list is: 1, 3, 7, 21, 49

This seems inconsistent. But notice:
- 49 = 7² → factors: 1, 7, 49
- 21 = 3×7 → factors: 1, 3, 7, 21

So perhaps this is actually Factors of 49 and Factors of 21, but it's mislabeled?

Wait — the label says "Factors of 49" twice? That doesn't make sense.

But the list includes 3 and 21, which are not factors of 49.

So likely, it’s a mistake in the labeling.

Looking closely at the image: It says:

> Factors of 49
> Factors of 49

But the box below has: 1, 3, 7, 21, 49

But 3 and 21 are not factors of 49.

So this must be Factors of 49 and Factors of 21 — but the labels are wrong.

Alternatively, maybe it's Factors of 49 and Factors of 21, but written incorrectly.

But let’s assume it's Factors of 49 and Factors of 21, since the list makes sense for those two.

Let’s proceed with that assumption.

Assumption: This Venn is for Factors of 49 and Factors of 21

- Factors of 49: 1, 7, 49
- Factors of 21: 1, 3, 7, 21

Common factors: 1, 7
Only in 49: 49
Only in 21: 3, 21

Venn Diagram:
- Left (49): 49
- Intersection: 1, 7
- Right (21): 3, 21

But wait — the labels say "Factors of 49" and "Factors of 49" — so that can't be.

Wait — maybe it's Factors of 49 and Factors of 49 — then all factors are same.

But the list includes 3 and 21 — which aren't factors of 49.

So clearly, this is a labeling error.

Alternatively, perhaps it's Factors of 49 and Factors of 21, and the second label should be “Factors of 21”.

But since the problem gives us the list: 1, 3, 7, 21, 49 — and asks us to place them, we can deduce:

Let’s suppose the two sets are:
- A: Factors of 49 → 1, 7, 49
- B: Factors of 21 → 1, 3, 7, 21

Then:
- Intersection: 1, 7
- Only A: 49
- Only B: 3, 21

So even if the label says "Factors of 49" twice, it's likely a typo.

We'll go with that.

---

4. Factors of 15 and Factors of 18

Given factors:
- Factors of 15: 1, 3, 5, 15
- Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 3
Only in 15: 5, 15
Only in 18: 2, 6, 9, 18

Venn Diagram:
- Left (15): 5, 15
- Intersection: 1, 3
- Right (18): 2, 6, 9, 18

---

Final Part: Write labels for the right and left sections of the Venn diagram.

There’s a separate Venn diagram with numbers placed:

```
3 4
/ \
6 12
\ /
2 10
\ /
5
```

Wait — the diagram shows:

- Left circle: 3, 4, 6, 12
- Right circle: 2, 5, 10
- Intersection: ?

Wait — let’s interpret the diagram properly.

From the image description:

It shows:
- Left circle: 3, 4, 6, 12
- Right circle: 2, 5, 10
- Intersection: 2 and 10? No — 2 and 10 are in the right side.

Wait — actually, the diagram is drawn as:

```
3 4
/ \
6 12
/ \
2 10
\ /
5 ?
```

No — better to look at standard layout.

The diagram is:

- Left circle: 3, 4, 6, 12
- Right circle: 2, 5, 10
- Intersection: 2 and 10? But 2 and 10 are only in right.

Wait — the numbers are:

- Left: 3, 4, 6, 12
- Right: 2, 5, 10
- Overlap: ??? — nothing shown in overlap?

Wait — no — the numbers are:

From the image:

- In left circle: 3, 4, 6, 12
- In right circle: 2, 5, 10
- In intersection: ??? — actually, the number 2 is at the bottom, shared?

Wait — let's read carefully:

The diagram has:

- Top-left: 3, 4
- Bottom-left: 6, 12
- Top-right: 5
- Bottom-right: 10
- Center (overlap): 2

Ah! So:

- Left circle: 3, 4, 6, 12, and 2 (in center)
- Right circle: 5, 10, and 2 (in center)
- So intersection: 2
- Left-only: 3, 4, 6, 12
- Right-only: 5, 10

So the numbers are:

- Left circle: 3, 4, 6, 12, 2
- Right circle: 2, 5, 10
- Intersection: 2

Now, what could these represent?

List of numbers: 2, 3, 4, 5, 6, 10, 12

Let’s see possible factor sets.

Notice:
- 2, 3, 4, 6, 12 — these are all factors of 12
- 2, 5, 10 — factors of 10?

But 3, 4, 6, 12 are not factors of 10.

Wait — maybe:

Left: Factors of 12 → 1, 2, 3, 4, 6, 12 — but 1 is missing

Right: Factors of 10 → 1, 2, 5, 10 — 1 missing

But in diagram, 1 is not present.

So perhaps not.

Alternative idea: Maybe the sets are even numbers and multiples of 3?

Check:

- Even numbers: 2, 4, 6, 10, 12 → yes
- Multiples of 3: 3, 6, 12 → also 3, 6, 12

But 3 is not even.

In diagram:
- Left: 3, 4, 6, 12 — includes odd 3
- Right: 2, 5, 10 — includes odd 5

Not helpful.

Another idea: Factors of 12 and factors of 10

- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 10: 1, 2, 5, 10

Common: 1, 2

But 1 is missing from diagram.

So maybe the sets are numbers less than 15 or something.

Wait — let's look at the numbers again:

Left circle: 3, 4, 6, 12, and 2 (in center)

Right circle: 2, 5, 10

So:
- Left: 2, 3, 4, 6, 12
- Right: 2, 5, 10
- Intersection: 2

So the numbers are:
- Left: 2, 3, 4, 6, 12
- Right: 2, 5, 10
- Only left: 3, 4, 6, 12
- Only right: 5, 10
- Both: 2

Now, think about factors of 12: 1, 2, 3, 4, 6, 12 — matches left set except missing 1

Similarly, factors of 10: 1, 2, 5, 10 — matches right except missing 1

So likely, the sets are factors of 12 and factors of 10, and 1 is omitted.

But the instruction says: “Write labels for the right and left sections of the Venn diagram.”

So probably:

- Left: Factors of 12
- Right: Factors of 10

But why is 1 missing? Maybe it's assumed or excluded.

Alternatively, maybe it's multiples of 2 and multiples of 3?

Multiples of 2: 2, 4, 6, 10, 12 — yes
Multiples of 3: 3, 6, 12 — yes
Intersection: 6, 12

But in diagram, intersection is only 2 — not matching.

Wait — no, intersection is 2.

But 2 is not a multiple of 3.

So no.

Another idea: Even numbers and numbers divisible by 2 and 3?

Wait — let’s try factors of 12 and factors of 10.

- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 10: 1, 2, 5, 10

Common: 1, 2

But in diagram, only 2 is in center — 1 is missing.

So maybe the numbers listed are just the ones used, and 1 is excluded.

So perhaps the labels are:

- Left: Factors of 12
- Right: Factors of 10

But let’s check if any other pair works.

Wait — what if it’s factors of 24 and factors of 10?

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 — too many.

Too big.

Alternatively, factors of 12 and factors of 10 is most plausible.

But why is 1 missing?

Perhaps it's because the problem wants only numbers greater than 1?

Or maybe it's a different interpretation.

Wait — another possibility: numbers that divide 12 and numbers that divide 10 — same thing.

So I think it's safe to say:

- Left: Factors of 12
- Right: Factors of 10

And the intersection is 2 (since 1 is missing).

But 1 divides both, so it should be there.

Unless the list is incomplete.

Wait — maybe the numbers are common multiples?

But 2, 3, 4, 5, 6, 10, 12 — not multiples.

Another idea: divisors of 12 and divisors of 10

Same as factors.

So likely, the intended labels are:

- Left: Factors of 12
- Right: Factors of 10

Even though 1 is missing, it might be an oversight.

Alternatively, maybe it’s even numbers and odd numbers?

But 2 is even, 3, 5 are odd — but 4, 6, 12 are even — so left has both even and odd? No.

Left has 3 (odd), 4,6,12 (even), 2 (even) — so not consistent.

So not that.

Wait — what if it's factors of 12 and factors of 10, and the diagram omits 1?

Then:

- Left: 2, 3, 4, 6, 12 → all factors of 12 except 1
- Right: 2, 5, 10 → all factors of 10 except 1
- Intersection: 2

Yes — that fits.

So the labels should be:

- Left: Factors of 12
- Right: Factors of 10

---

✔ Final Answers:

#### 1. Factors of 21 and Factors of 24
- Left (21): 7, 21
- Intersection: 1, 3
- Right (24): 2, 4, 6, 8, 12, 24

#### 2. Factors of 16 and Factors of 20
- Left (16): 8, 16
- Intersection: 1, 2, 4
- Right (20): 5, 10, 20

#### 3. Factors of 49 and Factors of 21 *(assuming typo)*
- Left (49): 49
- Intersection: 1, 7
- Right (21): 3, 21

#### 4. Factors of 15 and Factors of 18
- Left (15): 5, 15
- Intersection: 1, 3
- Right (18): 2, 6, 9, 18

#### Last Venn Diagram Labels:
- Left: Factors of 12
- Right: Factors of 10

(With the understanding that 1 is missing from both, but implied.)

---

🟩 Summary:

| Venn | Left | Intersection | Right |
|------|------|--------------|-------|
| 21 & 24 | 7, 21 | 1, 3 | 2, 4, 6, 8, 12, 24 |
| 16 & 20 | 8, 16 | 1, 2, 4 | 5, 10, 20 |
| 49 & 21 | 49 | 1, 7 | 3, 21 |
| 15 & 18 | 5, 15 | 1, 3 | 2, 6, 9, 18 |

Final labels for last diagram:
- Left: Factors of 12
- Right: Factors of 10

✔ Problem solved.