What are Multiples? How to Find Multiples of a Number?

When one number is multiplied by another, the result is called a multiple. If we say 4 × 2 = 8, for example, 8 is a multiple of 4 and 2. The other four-digit multiples are 4 (4 × 1 = 4), 8 (4 × 2 = 8), 12 (4 × 3 = 12), and so on. Let’s get started learning about multiples, which will enable us to understand a variety of other math concepts.

What are Multiples?

When you multiply one whole number by another whole number, you get multiple. In other words, when you multiply a number, you get its multiples! Can you recall the multiplication tables from school? We’ll use them to look for multiples. While listing the first five multiples of the number 4, let’s see how it helps us grasp the definition of multiples. The initial existing four multiples of 4 are 4, 8, 12, 16.

Properties of Multiples

The essential properties of multiples tell us a lot about them in brief. Here are a few primary and fundamental properties of multiples that tell us about the nature and behavior of multiples:

  1. Every number in the whole number system is a multiple of itself. For example, the first multiple of 3 is 3 itself as 3 × 1 = 3.
  2. The multiples of any number in the number system are infinite.
  3. We all know that numbers are infinite in nature. Hence, the multiples of a number are always infinite. For instance, if we need to note down all the multiples of 2, we start with 2 itself and then so on. However, will one be able to list all the multiples in one sitting? No, that is not possible because they are infinite.
  4. The multiple of any number on the number line is always greater than or equal to the number itself.

How to Find the Multiples of any Given Number?

Keeping the Concept Crisp and Brief

When naming the multiples of any given number, the students often forget to include the number itself and are mostly confused about whether or not to include the number zero. The multiples of 2 include 2 times an integer in the number system, including 2 × 0 and 2 × 1. So in this instance, 2 “is a multiple of 2” as well as 4 “is a multiple of 4”. The number zero is a multiple of every number in the number system and thus, it is an even number. When asked for the “smallest” multiple present on the number line or also named as the least common multiple, the implication and methodology are that only positive multiples are used. Thus number 6 is the “least” common multiple of 3 and 2 even though 0 and –6 are also multiples that 3 and 2 have in common in their factors, and they are less than 6 in value.

Keeping the Language Easy

It is not accurate to refer to a number as “a multiple” without saying which number it is a multiple of. The number 10 is “a multiple of 2” or “a multiple of 5” but not just a multiple in general. Numbers are always multiples of something and not just individual multiples. Also, 4 is a factor of 8, not a multiple of 8. And 8 is a multiple of 4, not a factor of 4.

A Fine Point

The term multiple means like factor and divisible. It is widely used only to refer to results of multiplication by a whole number in the entire number system.

Conclusion

Multiples are very easy and simple to understand and grasp. Every mathematical concept needs constant and persistent practice, to excel in academics. Multiples help students with quicker multiplication and division operations. Cuemath is an online learning platform that provides numerous exercises based on multiples that are absolutely free!