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What Are Rectangular Numbers? - Definition & Examples

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  • 0:00 What Are Rectangular Numbers?
  • 1:05 Other Rectangular Numbers
  • 1:37 Building Rectangular Numbers
  • 2:42 Lesson Summary
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Lesson Transcript
Instructor: Rayna Cummings

Rayna has taught Elementary Education for 12 years (in both 1st, 2nd, and 3rd grades) and holds a M.Ed in Early Childhood Education from The Ohio State University

Did you know there are numbers that when put in a certain order can form shapes? In this lesson, we are going to look at numbers, known as rectangular numbers, that when put in a certain order form a. . . rectangular shape! So, let's get learning and find those special numbers!

What Are Rectangular Numbers?

Well, you know a zero has an oval shape, but are you having a hard time figuring out what number looks like a rectangle? Don't worry, there isn't one! Rectangular numbers are special numbers that can be shown by making the shape of a rectangle using an array, which is objects placed in an arranged order using rows and columns.

Picture of a Rectangle
rectangle

Look at the rectangle and try to imagine the number of objects you can use in an array form to fill that rectangle evenly. Some numbers you should have came up with are 2, 6, and 8. Most even numbers, or numbers ending in 0, 2, 4, 6, or 8, can form a rectangular shape.

The number 2 is a rectangular number because it is 1 row by 2 columns. The number 6 is a rectangular number because it is 2 rows by 3 columns, and the number 8 is a rectangular number because it is 2 rows by 4 columns.

However, 4 is the only even number that cannot form a rectangular shape because it forms a square with an array of 2 rows by 2 columns. See?

Example of a square number
Square number

Other Rectangular Numbers

Even numbers are not the only rectangular numbers, there are also some odd numbers, or numbers ending in 1, 3, 5, 7, or 9, that can be put an array to form a rectangular shape. Can you think of any odd numbers that can be used in an array to form a rectangle shape?

Take a look at this picture and count the number of circles in the rectangle. How many circles can you count?

Odd rectangular number
Odd Rectangular Number

If you counted 15 circles, you are right. 15 is an odd rectangular number with an array of 3 rows by 5 columns.

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