Factor Matrix Chart
Multiplication Matrix
Grade 6 Math
Factors, Multiples, Perfect Squares & Number Patterns (1–12)
Diagonal = Perfect Squares (\(n^2\))
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
Perfect Squares & Exponents
Base multiplied by itself: \(a^2 = a \times a\) • Inverse: \(\sqrt{a^2} = a\)
1²
1
2²
4
3²
9
4²
16
5²
25
6²
36
7²
49
8²
64
9²
81
10²
100
11²
121
12²
144
Divisibility Rules
- 2: Last digit is even (0, 2, 4, 6, 8)
- 3: Sum of digits divisible by 3
- 4: Last 2 digits divisible by 4
- 5: Last digit is 0 or 5
- 6: Divisible by both 2 and 3
- 8: Last 3 digits divisible by 8
- 9: Sum of digits divisible by 9
- 10: Last digit is 0
Test 360: Even (✓ 2), 3+6+0=9 (✓ 3 & 9), ends in 0 (✓ 5 & 10).
GCF & LCM Concepts
Factor: Whole numbers that divide evenly into \(N\).
Factors of 18: 1, 2, 3, 6, 9, 18
Multiple: Product of \(N\) and any integer.
Multiples of 6: 6, 12, 18, 24, 30...
GCF: Greatest common factor for simplifying fractions.
LCM: Least common multiple for finding common denominators.
\(\text{GCF}(12, 18) = 6\)
\(\text{LCM}(12, 18) = 36\)
Primes & Properties
Prime Numbers (\(\le 50\)):
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
2 is the only even prime number.
Commutative Symmetry:
\(a \times b = b \times a\). The upper right half perfectly mirrors the lower left half across the diagonal!
Even × Any = Even Odd × Odd = Odd