Multiplication Squares with Answer Key - Intermediate ... - Free Printable

You're working on Multiplication Square Puzzles — a great way to practice factoring and multiplication! The goal is to fill in the 2x2 grid so that:

- The product of the two numbers in each row equals the number to the right of that row.
- The product of the two numbers in each column equals the number below that column.

Let’s solve each puzzle one by one, using logic and factor pairs.

---

✔ Example (for reference):

```
[12][2] → 12×2 = 24
[3 ][7] → 3×7 = 21
↓ ↓
36 14 ← 12×3=36, 2×7=14
```

---

## 🔢 Let's Solve Each Puzzle

---

a.

Right: 99, 42
Bottom: 63, 66

We need to find numbers A, B, C, D such that:
- A × B = 99
- C × D = 42
- A × C = 63
- B × D = 66

Factor pairs:
- 99: (1,99), (3,33), (9,11)
- 42: (1,42), (2,21), (3,14), (6,7)
- 63: (1,63), (3,21), (7,9)
- 66: (1,66), (2,33), (3,22), (6,11)

Try A=9, B=11 → 9×11=99 ✓
Then A×C=63 → 9×C=63 → C=7
Then C×D=42 → 7×D=42 → D=6
Check B×D=11×6=66 ✓

✔ Solution:
```
[9 ][11]
[7 ][6 ]
```

---

b.

Right: 32, 72
Bottom: 48, 48

A×B=32, C×D=72, A×C=48, B×D=48

Factor pairs:
- 32: (1,32), (2,16), (4,8)
- 72: (1,72), (2,36), (3,24), (4,18), (6,12), (8,9)
- 48: (1,48), (2,24), (3,16), (4,12), (6,8)

Try A=4, B=8 → 4×8=32 ✓
A×C=48 → 4×C=48 → C=12
C×D=72 → 12×D=72 → D=6
B×D=8×6=48 ✓

✔ Solution:
```
[4 ][8 ]
[12][6 ]
```

---

c.

Right: 20, 15
Bottom: 10, 30

A×B=20, C×D=15, A×C=10, B×D=30

Try A=5, B=4 → 5×4=20 ✓
A×C=10 → 5×C=10 → C=2
C×D=15 → 2×D=15 → D=7.5 ✘ Not integer.

Try A=2, B=10 → 2×10=20 ✓
A×C=10 → 2×C=10 → C=5
C×D=15 → 5×D=15 → D=3
B×D=10×3=30 ✓

✔ Solution:
```
[2 ][10]
[5 ][3 ]
```

---

d.

Right: 16, 28
Bottom: 16, 28

A×B=16, C×D=28, A×C=16, B×D=28

Try A=4, B=4 → 4×4=16 ✓
A×C=16 → 4×C=16 → C=4
C×D=28 → 4×D=28 → D=7
B×D=4×7=28 ✓

✔ Solution:
```
[4 ][4 ]
[4 ][7 ]
```

---

e.

Right: 72, 84
Bottom: 96, 63

A×B=72, C×D=84, A×C=96, B×D=63

Try A=8, B=9 → 8×9=72 ✓
A×C=96 → 8×C=96 → C=12
C×D=84 → 12×D=84 → D=7
B×D=9×7=63 ✓

✔ Solution:
```
[8 ][9 ]
[12][7 ]
```

---

f.

Right: 36, 55
Bottom: 30, 66

A×B=36, C×D=55, A×C=30, B×D=66

55 factors: (5,11) — only integer pair.

Try B=5, D=11 → then B×D=55? Wait — C×D=55 → so C and D must be 5 and 11.

Try C=5, D=11 → C×D=55 ✓
A×C=30 → A×5=30 → A=6
A×B=36 → 6×B=36 → B=6
But then B×D=6×11=66 ✓

✔ Solution:
```
[6 ][6 ]
[5 ][11]
```

---

g.

Right: 56, 54
Bottom: 42, 72

A×B=56, C×D=54, A×C=42, B×D=72

Try A=7, B=8 → 7×8=56 ✓
A×C=42 → 7×C=42 → C=6
C×D=54 → 6×D=54 → D=9
B×D=8×9=72 ✓

✔ Solution:
```
[7 ][8 ]
[6 ][9 ]
```

---

h.

Right: 3, 72
Bottom: 18, 12

A×B=3, C×D=72, A×C=18, B×D=12

3 factors: (1,3)

Try A=1, B=3 → 1×3=3 ✓
A×C=18 → 1×C=18 → C=18
C×D=72 → 18×D=72 → D=4
B×D=3×4=12 ✓

✔ Solution:
```
[1 ][3 ]
[18][4 ]
```

---

i.

Right: 132, 132
Bottom: 144, 121

A×B=132, C×D=132, A×C=144, B×D=121

121 is 11² → so B and D must be 11 and 11.

Try B=11, D=11 → B×D=121 ✓
A×B=132 → A×11=132 → A=12
A×C=144 → 12×C=144 → C=12
C×D=12×11=132 ✓

✔ Solution:
```
[12][11]
[12][11]
```

---

j.

Right: 2, 12
Bottom: 3, 8

A×B=2, C×D=12, A×C=3, B×D=8

2 factors: (1,2)

Try A=1, B=2 → 1×2=2 ✓
A×C=3 → 1×C=3 → C=3
C×D=12 → 3×D=12 → D=4
B×D=2×4=8 ✓

✔ Solution:
```
[1 ][2 ]
[3 ][4 ]
```

---

k.

Right: 60, 63
Bottom: 54, 70

A×B=60, C×D=63, A×C=54, B×D=70

Try A=6, B=10 → 6×10=60 ✓
A×C=54 → 6×C=54 → C=9
C×D=63 → 9×D=63 → D=7
B×D=10×7=70 ✓

✔ Solution:
```
[6 ][10]
[9 ][7 ]
```

---

## 🎉 Final Answers:

a.

```
9 11
7 6
```

b.

```
4 8
12 6
```

c.

```
2 10
5 3
```

d.

```
4 4
4 7
```

e.

```
8 9
12 7
```

f.

```
6 6
5 11
```

g.

```
7 8
6 9
```

h.

```
1 3
18 4
```

i.

```
12 11
12 11
```

j.

```
1 2
3 4
```

k.

```
6 10
9 7
```

---

✔ You’ve now solved all the puzzles! This reinforces understanding of factor pairs and multiplication relationships in a grid. Great job!

Let me know if you’d like these formatted as a printable answer key or want to check your own work against this!