**Factors And Multiples**

**Factors And Multiples**

Factors and multiples are always very confusing for children. Their interrelationship is rarely understood by kids and thus the struggle. Let’s first understand what do they mean?

**What is a factor?**

A factor of a number is the number that divides it completely without leaving any remainder.

**What is a multiple?**

When we multiply a number, with itself or other numbers, the result is nothing but the multiple of that number.

Example:

Let us take number 20.

To find its factors, we need to think of numbers that can divide 20 completely without leaving any remainder.

So 4,5,10,20,1 become the factors of 20.

Similarly, when we multiply 4 and 5, the result is 20. That means 4 and 5 are multiples of 20.

**An easy trick to teach:**

Whenever teaching factors of a number, ask “Which numbers can divide this number?” or “In which multiplication tables do we get this number?”

Whenever teaching multiplies, just say “You have to write the multiplication table of this number.”

**Highest common factor (HCF):**

HCF is the highest number from the list of common factors of given two or three numbers.

We always use HCF to equally divide the number such that there is no leftover.

** Lowest Common Multiple (LCM):**

- LCM is the smallest number that is a multiple of each of two or more numbers.
- LCM is used when in case of repetition, to predict when will the same thing happen again.

**Finding HCF using the listing method:**

- List all the factors of every number
- Identify the common factors that are common in all the numbers.
- Identify the highest common factor among the list of common factors.
- This is the HCF.

**Finding LCM using the listing method:**

- List the multiples of each number until at least one of the multiples appears on all lists.
- Find the smallest number that is on all of the lists.
- This number is the LCM.

**Math facts:**

- 1 is the factor of every number.
- 0 is also a multiple of every number.
- HCF is also called GCF (Greatest common factor) Different ways of teaching: Teaching through stories:

**Different ways of teaching: Teaching through stories:**