Factors and Multiples Table — Definition, Formula & Examples

A factors and multiples table is a reference chart that lists the factors (numbers that divide evenly into a given number) and the first several multiples (products of a given number) for a set of whole numbers, typically 1 through 20 or beyond.

A tabular arrangement in which each row corresponds to a positive integer $n$ and displays both the complete set of divisors of $n$ and a finite list of successive products $n, 2n, 3n, \dots$ , serving as a compact lookup tool for divisibility and multiplication facts.

How It Works

Each row of the table starts with a number

n

. In one column you list every whole number that divides

n

with no remainder — those are the factors. In another column you list the products

n \times 1, n \times 2, n \times 3, \dots

— those are the multiples. To find whether 6 is a factor of 18, scan the row for 18 and check the factors column. To find common multiples of two numbers, compare their multiples columns and look for shared values.

Worked Example

Problem: Use a factors and multiples table to list the factors and the first five multiples of 12.

Find factors: Test which whole numbers from 1 to 12 divide 12 evenly.

12 \div 1 = 12,\; 12 \div 2 = 6,\; 12 \div 3 = 4,\; 12 \div 4 = 3,\; 12 \div 6 = 2,\; 12 \div 12 = 1

List factors: The factors of 12 are all the divisors found above.

\{1,\, 2,\, 3,\, 4,\, 6,\, 12\}

List first five multiples: Multiply 12 by 1 through 5.

12,\; 24,\; 36,\; 48,\; 60

Answer: Factors of 12: {1, 2, 3, 4, 6, 12}. First five multiples of 12: 12, 24, 36, 48, 60.

Why It Matters

Having a factors and multiples table on hand speeds up work with greatest common factors and least common multiples, two skills tested heavily in 4th–6th grade math. It also builds the number sense needed for simplifying fractions and solving word problems involving divisibility.

Common Mistakes

Mistake: Confusing the factors column with the multiples column — for example, listing 24 and 36 as factors of 12 instead of as multiples.

Correction: Factors of

n

are always less than or equal to

n

. Multiples of

n

are always greater than or equal to

n

. Keep the two columns clearly labeled.