A multiplication table is a grid that lists the products of pairs of numbers, usually 1 to 10 or 1 to 12. To read it, find one factor along the top row and the other down the left column; the box where they meet is the product. Row 6 meets column 7 at 42, since 6 × 7 = 42.
Go across row 6 and down column 7 until they meet: 6 × 7 = 42. The yellow diagonal holds the square numbers.
Formal definition and notation
A multiplication table for the numbers 1 to n is an n by narray whose entry in row i and column j is the product i × j. Because i × j = j × i, the table is symmetric about its main diagonal, and the diagonal entries 1, 4, 9, …, n2 are the square numbers. Each row i lists the first n multiples of i.
Symbol
Read it as
Meaning
i × j
i times j
the entry where row i meets column j
Key facts
Each row (or column) is the skip-counting list for its number: row 4 reads 4, 8, 12, 16, …
The table is symmetric across the diagonal, because a × b = b × a. That cuts the 100 facts of a 10 by 10 table to 55 different ones.
The diagonal from top left to bottom right holds the square numbers 1, 4, 9, 16, …
Every entry in an even row or column is even; odd times odd is the only way to get an odd product.
In row 9, the digits of each product add to 9 (18, 27, 36, …, 81), and the tens digit goes up as the ones digit goes down.
Read it backward to divide: in row 8, find 56; its column is 7, so 56 ÷ 8 = 7.
Try it: one fact as a rectangle
Interactive
Every box in a multiplication table is a rectangle of squares. Make 8 by 7 and count: 56. Then try 7 by 8 to see why the table is symmetric.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Multiplication Table examples, step by step
Example 1: Read a product
Warm-up
Use a multiplication table to find 8 times 9.
Find 8 in the left column and 9 in the top row.
Follow row 8 across to column 9.
The box shows 72.
Answer:8 × 9 = 72
Example 2: Divide with the table
Core
Use the table to find 63 ÷ 7.
Go to row 7.
Move across until you reach 63.
63 is in column 9, so 7 × 9 = 63 and 63 ÷ 7 = 9.
Answer:63 ÷ 7 = 9
Example 3: Count appearances
Test-style
In a 1 to 10 multiplication table, how many boxes contain 24?
List factor pairs of 24 with both factors from 1 to 10: 3 × 8, 4 × 6, 6 × 4, 8 × 3.
2 × 12 and 1 × 24 are not in the table, because 12 and 24 are greater than 10.
That is 4 boxes.
Answer: 24 appears in 4 boxes.
Common mistakes
✗ MistakeReading row 7 to column 8 and landing in the box beside it: 7 × 8 = 54.
✓ InsteadTrace carefully with two fingers: 7 × 8 = 56.
Slipping one box gives a neighbor product. Check with a related fact: 7 × 8 = 7 × 4 × 2 = 28 × 2 = 56.
✗ MistakeAdding the row and column: row 5, column 6 gives 11.
✓ InsteadThe table holds products: 5 × 6 = 30.
An addition table looks similar; in a multiplication table the entries multiply.
Not to be confused with
Multiplication Tablevs.Addition table
An addition table has sums in its boxes: row 5, column 6 holds 11. A multiplication table holds 30 there.
A fact family is one set of related facts (6, 7, 42). The multiplication table shows every fact at once.
Quick check: 3 questions
Question 1 of 3
In a multiplication table, what is in row 7, column 6?
Show answer and explanation
Answer: C.7 × 6 = 42. 13 adds the numbers, 48 is 6 × 8, and 36 is 6 × 6, one box over.
Question 2 of 3
Which numbers are on the main diagonal of a multiplication table?
Show answer and explanation
Answer: A. The diagonal holds 1 × 1, 2 × 2, 3 × 3 and so on, the square numbers 1, 4, 9, 16. It contains odd numbers like 9, no prime numbers, and at most one multiple of 10 (100).
Question 3 of 3
Row 4 of a 1 to 12 table reads 4, 8, 12, … What is the last number in that row?
Show answer and explanation
Answer: D. The last column is 12, so the entry is 4 × 12 = 48. 40 and 44 stop at columns 10 and 11, and 16 is 4 × 4.
Multiplication Table: frequently asked questions
What is the fastest way to learn the multiplication table?
Learn the easy rows first (0, 1, 2, 5, 10), then use symmetry: knowing 3 × 8 gives 8 × 3. Of the 100 facts in a 10 by 10 table, only a few dozen remain after that. Build them from known facts, such as 6 × 7 = 5 × 7 + 7 = 42, and practice a little every day. The Common Core expects these facts from memory by the end of grade 3.
Why is the multiplication table symmetric?
Because multiplication is commutative: 4 × 9 and 9 × 4 both equal 36. The box in row 4, column 9 and the box in row 9, column 4 always match, so if you fold the table along the diagonal of square numbers, the two halves line up exactly.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 3.OA.C.7, CCSS 3.OA.D.9
Cite this entry
Effortless Math Team. “Multiplication Table.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/multiplication-table/
Flashcard
TermMultiplication Tablerow × column = box
DefinitionA grid of products. Find one factor on the top and one on the side; they meet at the product, as with 6 × 7 = 42.
ProductThe product is the answer you get when you multiply two or more numbers. In 4 × 6 = 24, the product is 24, and 4 and 6 are the factors. In word problems, the words “product of” always mean multiply, so “the product of 3 and 7” is 21.Operations · Grade 3, Grade 4, Grade 5NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2ArrayAn array is an arrangement of objects in equal rows and equal columns, forming a rectangle. A 4 by 6 array has 4 rows of 6, so it holds 4 × 6 = 24 objects. Arrays show multiplication as equal groups, and turning one sideways shows that 4 × 6 = 6 × 4.Operations · Grade 2, Grade 3, Grade 4Square NumberA square number is the result of multiplying a whole number by itself. The first square numbers are 1, 4, 9, 16, 25 and 36, because 1 × 1 = 1, 2 × 2 = 4, 3 × 3 = 9 and so on. That many dots fill a square exactly, like 16 dots in a 4 by 4 square.Operations · Grade 3, Grade 4, Grade 5Factor PairA factor pair is two whole numbers that multiply to give a certain number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4. Listing factor pairs is a sure way to find every factor of a number: start at 1 and stop once the pairs begin to repeat.Number System · Grade 4, Grade 5, Grade 6AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2Fact FamilyA fact family is a group of related math facts that use the same three numbers. With 6, 9 and 15 you get 6 + 9 = 15, 9 + 6 = 15, 15 − 6 = 9 and 15 − 9 = 6. Multiplication and division make fact families too, such as 4, 7 and 28. They show that operations undo each other.Operations · Grade 1, Grade 2, Grade 3SymmetrySymmetry is when a shape matches itself after it is flipped or turned. A shape has line symmetry when a line splits it into two mirror-image halves that match exactly when folded; that fold line is the line of symmetry. It has rotational symmetry when it looks the same after a turn of less than 360°.Geometry · Grade 4, Grade 8, GeometryMultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4Repeated AdditionRepeated addition is adding the same number again and again. It is one way to understand multiplication: 3 + 3 + 3 + 3 = 4 × 3 = 12. The number of times you add is one factor, and the number being added is the other. It only works when all the addends are equal.Operations · Grade 2, Grade 3DivisionDivision is the operation of splitting a number into equal groups. In 12 ÷ 3 = 4, the dividend 12 is shared into 3 equal groups (the divisor), and each group gets 4 (the quotient). Division undoes multiplication, because 3 × 4 = 12. If the groups do not come out even, the amount left over is the remainder.Operations · Grade 3, Grade 4, Grade 5Commutative PropertyThe commutative property says that changing the order of the numbers does not change the result of adding or multiplying them: a + b = b + a and a × b = b × a. For example, 4 + 9 = 9 + 4 and 3 × 5 = 5 × 3. Subtraction and division are not commutative.Operations · Grade 1, Grade 3, Grade 6Skip CountingSkip counting is counting forward or backward by the same number each time instead of by 1, such as 2, 4, 6, 8 or 5, 10, 15, 20. Each jump adds the same amount, so skip counting by 5 six times reaches 6 × 5 = 30. It is a quick way to count groups and learn multiplication facts.Number System · Kindergarten, Grade 1, Grade 2MultipleA multiple of a number is the result of multiplying that number by any whole number. The multiples of 4 are 4, 8, 12, 16, and so on, continuing without end. Every number is a multiple of itself and of 1. To test a number, divide: if the remainder is 0, it is a multiple.Number System · Grade 4, Grade 5, Grade 6