Multiplication chart 1–30
Every product from 1 × 1 to 30 × 30 on one page: 900 answers. This 30x30 multiplication chart, also called a multiplication table, is a free PDF in Letter or A4.
900 answers on one pageUpdated
- Grid
- 30 × 30
- Products
- 900
- Largest product
- 900
- Squares on the diagonal
- 30
- Different numbers
- 308
Patterns in the 1–30 chart
The diagonal of squares
From the top left to the bottom right the chart reads 1, 4, 9, 16 and on to 900. The steps between them are the odd numbers: 3, 5, 7, 9.
24 × 24 = 576 · 27 × 27 = 729 · 30 × 30 = 900Two halves that match
The chart is a mirror across the diagonal, because 7 × 27 and 27 × 7 are the same. That leaves 465 facts to learn, not 900.
435 mirrored pairs + 30 squares = 465The numbers that repeat
Only 308 different numbers fill the 900 squares. None appears more than ten times; 60 and 120 do.
60 = 2 × 30 · 3 × 20 · 4 × 15 · 5 × 12 · 6 × 10Rows 20 and 30
Row 20 is row 2 with a zero on the end, and row 30 is row 3 with a zero. The same shortcut turns any tens number into a single-digit fact.
30 × 7 = 3 × 7 × 10 = 210
Other multiplication charts
Multiplication chart 1–30 FAQ
How many facts are on a 1–30 multiplication chart?
900, one for each square of the 30 × 30 grid. Because the order of the two numbers does not matter, 465 of them are different facts.
What is the biggest number on the chart?
900, in the bottom right corner, from 30 × 30.
Does it fit on one page?
Yes. The PDF is one portrait page in Letter or A4, with the site footer outside the grid. The numerals are small at this size, so print at 100% scale.
How do I read it?
Find the first number down the left side and the second along the top. The square where that row and column meet holds the answer.