Multiples of 11 Explained for Students

The concept of Multiples of 11 is a core part of the number system in mathematics. Knowing how to find and work with multiples helps in solving a wide range of arithmetic, algebra, and divisibility problems. Understanding this topic is essential for competitive exams like JEE, NEET, and for mastering school maths.

What Are Multiples of 11?

A multiple of 11 is any number that can be written as 11 multiplied by another whole number (also called an integer). For example, 22, 33, 44, and 55 are all multiples of 11 because they can be written as 11 × 2, 11 × 3, 11 × 4, and 11 × 5, respectively. The multiples of any number form patterns that are widely used in topics like algebra, factors and multiples, and divisibility rules. This foundational concept will help students tackle more advanced maths easily.

Formula and Method to Find Multiples of 11

To find multiples of 11, use this simple formula:

Multiple = 11 × n, where n is a whole number (n = 1, 2, 3, ...).

For example:

• First multiple: 11 × 1 = 11
• Second multiple: 11 × 2 = 22
• Third multiple: 11 × 3 = 33
• And so on…

Another way is repeated addition: 11, 11+11=22, 22+11=33, etc. Recognizing this pattern helps with number sequences and problem-solving in arithmetic and algebra.

List of Multiples of 11 (First 20)

Below is a list of the first 20 multiples of 11 to help with quick revision and identification:

To find even more multiples, keep increasing n by 1 each time. For a full list up to 100 or 1000, just use the formula!

Worked Examples

Let’s solve a few sample problems involving multiples of 11 to see how this concept is used:

Example 1: List the multiples of 11 less than 100.

1. Start from 11 × 1 = 11.
2. Keep increasing n: 11, 22, 33, 44, 55, 66, 77, 88, 99.
3. Next multiple is 110, which is more than 100, so stop.
4. So, the multiples of 11 less than 100 are: 11, 22, 33, 44, 55, 66, 77, 88, 99.

Example 2: Is 253 a multiple of 11?

1. Divide 253 by 11: 253 ÷ 11 = 23. So, 11 × 23 = 253.
2. 253 is exactly divisible by 11, so yes, 253 is a multiple of 11.

Example 3: Find the 15th multiple of 11.

1. Use the formula: 11 × 15 = 165.

Practice Problems

• List the first 10 multiples of 11.
• Is 462 a multiple of 11?
• Find the sum of the first five multiples of 11.
• Between 200 and 350, how many multiples of 11 are there?
• What is the 25th multiple of 11?

Common Mistakes to Avoid

• Confusing multiples of 11 with factors of 11. (Multiples are products, factors divide exactly!)
• Forgetting to start at 11 × 1 when listing multiples.
• Thinking that multiples must be less than 100 or 1000. In fact, multiples go on forever!
• Mistaking a number like 101 (which is not 11 × n for an integer n) as a multiple.

Real-World Applications

Multiples of 11 are commonly seen in real-life scenarios such as:

• Arranging items in equal groups (for example, packing 11 pens per box in a factory).
• Divisibility checks in coding and banking to catch errors in long numbers (using the divisibility rule for 11).
• Understanding patterns in multiplication tables and mental maths speed tricks.

Many math puzzles, competitive exam problems, and topics like Factors and Multiples and Number System use the idea of multiples. At Vedantu, we simplify such concepts with videos, tables, and examples so every student can master arithmetic basics quickly.

In this topic, we explored Multiples of 11, how to find them using formulas, and their patterns. Knowing the difference between multiples and factors, working with tables and patterns, and applying them to everyday scenarios helps you develop strong number sense for exams and daily life. For more learning, check out related topics on Factors of 11, Table of 11, and other numbers on Vedantu’s math portal.