Why should I memorize multiplication tables?

Memorizing multiplication tables builds number fluency, speeds up mental math, and is essential for algebra, fractions, factoring, and standardized tests. Students who know their tables can focus on higher-level problem-solving instead of getting stuck on basic arithmetic.

What is the fastest way to memorize times tables?

Use a mix of strategies: learn the easy tables first (1, 2, 5, 10, 11), apply tricks for 9s (finger method) and numbers ending in 5 (squaring shortcut), use decomposition for larger numbers (e.g., 13 × 7 = 10×7 + 3×7), and practice with timed drills and flashcards regularly.

How many perfect squares are there from 1 to 625?

There are 25 perfect squares from 1² = 1 to 25² = 625. Perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625.

What is the difference between a square and a cube of a number?

A square (n²) is a number multiplied by itself once (e.g., 5² = 25). A cube (n³) is a number multiplied by itself twice (e.g., 5³ = 125). Geometrically, n² is the area of a square with side n, and n³ is the volume of a cube with side n.

Is there a shortcut for squaring numbers ending in 5?

Yes! For any number ending in 5: take the tens digit, multiply it by (tens digit + 1), then append 25. Example: 35² → 3 × 4 = 12, append 25 → 1225. This works because (10a + 5)² = 100a(a+1) + 25.

MathematicsHigh School

Multiplication Tables, Squares & Cubes

Master the multiplication tables from 1 to 25, along with their squares and cubes. Use the interactive explorer below to study each number, learn memory tricks, and test yourself with the reference grids and quiz.

Introduction

Why learn these?

Multiplication fluency is the foundation of all higher math — from simplifying fractions and factoring polynomials to calculus. Students who can instantly recall products, squares, and cubes solve problems faster, make fewer errors, and build stronger number sense.

Tables (× 1–12)

Perfect Squares

Perfect Cubes

Number Explorer

Select a number to explore its table, square, and cube:

Square

7² = 49

Cube

7³ = 343

7² = 49 — "Seven ate (7×8=56) minus seven = 49"

7³ = 343 — palindrome!

Table of 7

7	×	1	=	7
7	×	2	=	14
7	×	3	=	21
7	×	4	=	28
7	×	5	=	35
7	×	6	=	42
7	×	7	=	49
7	×	8	=	56
7	×	9	=	63
7	×	10	=	70
7	×	11	=	77
7	×	12	=	84

Memory Tricks for 7

Use anchor facts you know well, then add or subtract 7 to reach nearby products.

7 × 7 = 49 (anchor)

7 × 8 = 49 + 7 = 56 ("5,6,7,8")

7 × 6 = 49 − 7 = 42

Quick Facts

Even or Odd?: Odd
Prime?: Yes
Factors: 1, 7
Last digit of n²: 9
Last digit of n³: 3

Multiplication Tricks

The 9s Finger Trick

Hold up both hands (10 fingers). To find 9 × N, fold down finger #N from the left. Count the fingers to the left of the folded finger for the tens digit, and fingers to the right for the ones digit.

9 × 4 = 36

The 11s Pattern

For single digits: 11 × N = NN (repeat the digit). For two-digit numbers: split the digits and put their sum in the middle.

Example: 11 × 36 = 3_(3+6)_6 = 396

Decomposition Strategy

Break a hard problem into easier parts. For any number 10+: split into (10 × N) + (remainder × N).

Example: 17 × 6 = (10 × 6) + (7 × 6) = 60 + 42 = 102

Multiply by 25

Since 25 = 100 ÷ 4, multiply by 100 first, then divide by 4. Works fast for even numbers.

Example: 25 × 16 = 1600 ÷ 4 = 400

Double & Halve

When one number is hard, double it and halve the other. The product stays the same.

Example: 14 × 15 = 7 × 30 = 210

Near-Tens Trick

For numbers near a multiple of 10 (like 19, 21), use the nearest ten and adjust.

Example: 19 × 8 = (20 × 8) − (1 × 8) = 160 − 8 = 152

Perfect Squares (n²)

A perfect square is the product of an integer with itself. Knowing squares up to 25² = 625 is invaluable for algebra, geometry, and mental estimation.

Squaring Shortcuts

Numbers ending in 5

Take the tens digit, multiply by (tens digit + 1), append 25. 35² → 3×4 = 12 → 1225

Near a known square

Use (a+b)² = a² + 2ab + b². 21² = 20² + 2(20)(1) + 1² = 400 + 40 + 1 = 441

Difference of squares

n² = (n−1)(n+1) + 1. 13² = 12 × 14 + 1 = 168 + 1 = 169

Last-Digit Patterns of Squares

The last digit of a perfect square only ever cycles through: 0, 1, 4, 5, 6, 9. No perfect square ever ends in 2, 3, 7, or 8.

Perfect Cubes (n³)

A perfect cube is a number multiplied by itself three times. Cubes appear in volume calculations, algebra (sum/difference of cubes), and physics.

Cube Patterns

Last digits of cubes

Unlike squares, cubes can end in any digit 0–9. In fact, the last digit of n³ is always the same as the last digit of n.

Sum of cubes formula

a³ + b³ = (a + b)(a² − ab + b²). Example: 2³ + 3³ = 8 + 27 = 35 = (2+3)(4−6+9) = 5 × 7 = 35

Nicomachus' theorem

The sum of the first n cubes equals the square of the sum of the first n natural numbers: 1³ + 2³ + … + n³ = (1 + 2 + … + n)²

Anchor Cubes to Memorize

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

7³ = 343

8³ = 512

9³ = 729

10³ = 1,000

12³ = 1,728

15³ = 3,375

20³ = 8,000

Reference Grids

	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
13	13	26	39	52	65	78	91	104	117	130	143	156
14	14	28	42	56	70	84	98	112	126	140	154	168
15	15	30	45	60	75	90	105	120	135	150	165	180
16	16	32	48	64	80	96	112	128	144	160	176	192
17	17	34	51	68	85	102	119	136	153	170	187	204
18	18	36	54	72	90	108	126	144	162	180	198	216
19	19	38	57	76	95	114	133	152	171	190	209	228
20	20	40	60	80	100	120	140	160	180	200	220	240
21	21	42	63	84	105	126	147	168	189	210	231	252
22	22	44	66	88	110	132	154	176	198	220	242	264
23	23	46	69	92	115	138	161	184	207	230	253	276
24	24	48	72	96	120	144	168	192	216	240	264	288
25	25	50	75	100	125	150	175	200	225	250	275	300

Hover to highlight row and column. Diagonal cells (in amber) are perfect squares.

Memory Aids

"5, 6, 7, 8" → 56 = 7 × 8

The digits form a counting sequence.

"I ate and ate until I was sick on the floor" → 8 × 8 = 64

Rhyming mnemonic for a tricky product.

Squares ending in 5: tens × (tens + 1), then append 25

45² = 4×5 = 20, append 25 → 2025.

The 9-times digit sum is always 9

9×3 = 27 → 2+7 = 9. Works up to 9×10 = 90.

Last digit of n³ follows a predictable cycle

The ones digit of n³ depends only on the ones digit of n. For example: 2→8, 3→7, 4→4, 7→3, 8→2. Once you learn the 10-digit cycle, you can instantly predict the last digit of any cube.

Nicomachus: (1+2+…+n)² = 1³+2³+…+n³

The sum of the first 5 cubes: 1+8+27+64+125 = 225 = 15² = (1+2+3+4+5)².

Common Mistakes

Mistake: Confusing 6 × 8 and 6 × 9

Fix: 6×8 = 48 (double 24), 6×9 = 54 (use the 9s trick: 10×6−6 = 54).

Mistake: Thinking n² means n × 2

Fix: n² means n × n, not n × 2. For example, 5² = 25, not 10.

Mistake: Mixing up 7 × 8 (56) and 7 × 9 (63)

Fix: Remember "5, 6, 7, 8" for 56 = 7×8. For 63, use the 9s finger trick.

Mistake: Forgetting to carry when using decomposition

Fix: 17 × 8: 10×8 = 80, 7×8 = 56, then 80 + 56 = 136 (not 1,316).

Mistake: Assuming n³ = 3 × n²

Fix: n³ = n × n × n, not 3 × n². For example, 4³ = 64, but 3 × 4² = 48.

Quick Revision Summary

✓Multiplication tables 1–12 for every number 1–25 — the core facts for math fluency.
✓Perfect squares from 1² = 1 to 25² = 625 — used in algebra, geometry, and estimation.
✓Perfect cubes from 1³ = 1 to 25³ = 15,625 — used in volume, factoring, and physics.
✓Memory tricks: finger method (9s), decomposition (split into tens + remainder), ends-in-5 shortcut for squares.
✓Last digit of a square is always 0, 1, 4, 5, 6, or 9 — never 2, 3, 7, or 8.
✓Last digit of n³ follows a repeating 10-digit cycle based on the last digit of n.
✓Nicomachus' theorem: 1³ + 2³ + … + n³ = (1 + 2 + … + n)².

Frequently Asked Questions

Why should I memorize multiplication tables?: Memorizing multiplication tables builds number fluency, speeds up mental math, and is essential for algebra, fractions, factoring, and standardized tests. Students who know their tables can focus on higher-level problem-solving instead of getting stuck on basic arithmetic.
What is the fastest way to memorize times tables?: Use a mix of strategies: learn the easy tables first (1, 2, 5, 10, 11), apply tricks for 9s (finger method) and numbers ending in 5 (squaring shortcut), use decomposition for larger numbers (e.g., 13 × 7 = 10×7 + 3×7), and practice with timed drills and flashcards regularly.
How many perfect squares are there from 1 to 625?: There are 25 perfect squares from 1² = 1 to 25² = 625. Perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625.
What is the difference between a square and a cube of a number?: A square (n²) is a number multiplied by itself once (e.g., 5² = 25). A cube (n³) is a number multiplied by itself twice (e.g., 5³ = 125). Geometrically, n² is the area of a square with side n, and n³ is the volume of a cube with side n.
Is there a shortcut for squaring numbers ending in 5?: Yes! For any number ending in 5: take the tens digit, multiply it by (tens digit + 1), then append 25. Example: 35² → 3 × 4 = 12, append 25 → 1225. This works because (10a + 5)² = 100a(a+1) + 25.

Practice Quiz

Test your recall of multiplication facts, squares, and cubes — select the correct answer for each question.

1.What is 7 × 8?

2.What is 12²?

3.What is 5³?

4.What is 9 × 7?

5.Which of these is a perfect square?

6.What is 15 × 15?

7.What is 4³?

8.What is 13 × 7?

9.What is 25²?

10.What is 3³ + 4³?

7	×	1	=	7
7	×	2	=	14
7	×	3	=	21
7	×	4	=	28
7	×	5	=	35
7	×	6	=	42
7	×	7	=	49
7	×	8	=	56
7	×	9	=	63
7	×	10	=	70
7	×	11	=	77
7	×	12	=	84

	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
13	13	26	39	52	65	78	91	104	117	130	143	156
14	14	28	42	56	70	84	98	112	126	140	154	168
15	15	30	45	60	75	90	105	120	135	150	165	180
16	16	32	48	64	80	96	112	128	144	160	176	192
17	17	34	51	68	85	102	119	136	153	170	187	204
18	18	36	54	72	90	108	126	144	162	180	198	216
19	19	38	57	76	95	114	133	152	171	190	209	228
20	20	40	60	80	100	120	140	160	180	200	220	240
21	21	42	63	84	105	126	147	168	189	210	231	252
22	22	44	66	88	110	132	154	176	198	220	242	264
23	23	46	69	92	115	138	161	184	207	230	253	276
24	24	48	72	96	120	144	168	192	216	240	264	288
25	25	50	75	100	125	150	175	200	225	250	275	300

7	×	1	=	7
7	×	2	=	14
7	×	3	=	21
7	×	4	=	28
7	×	5	=	35
7	×	6	=	42
7	×	7	=	49
7	×	8	=	56
7	×	9	=	63
7	×	10	=	70
7	×	11	=	77
7	×	12	=	84

	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
13	13	26	39	52	65	78	91	104	117	130	143	156
14	14	28	42	56	70	84	98	112	126	140	154	168
15	15	30	45	60	75	90	105	120	135	150	165	180
16	16	32	48	64	80	96	112	128	144	160	176	192
17	17	34	51	68	85	102	119	136	153	170	187	204
18	18	36	54	72	90	108	126	144	162	180	198	216
19	19	38	57	76	95	114	133	152	171	190	209	228
20	20	40	60	80	100	120	140	160	180	200	220	240
21	21	42	63	84	105	126	147	168	189	210	231	252
22	22	44	66	88	110	132	154	176	198	220	242	264
23	23	46	69	92	115	138	161	184	207	230	253	276
24	24	48	72	96	120	144	168	192	216	240	264	288
25	25	50	75	100	125	150	175	200	225	250	275	300