How to Find Factors of a Number?

This Math video lesson is designed for 6-12 years old children to help them understand how to find factors of a number using a pegboard.

What are the Factors?

Finding factors of a number is a fundamental concept in mathematics and is used in many mathematical operations. Factors are numbers that can divide a given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, as these numbers can divide by 12 without leaving a remainder.

In other words, a factor is a number that divides another number evenly. For example, 2 and 4 are factors of 8, because 8 divided by 2 is 4, and 8 divided by 4 is 2.

There are 2 different ways to find factors of a number.

Factor Tree: A factor tree is a diagram that shows all the factors of a number. To create a factor tree, start with the number at the top of the tree. Then, divide the number by its smallest prime factor. Write the prime factor below the number, and then divide the prime factor by its smallest prime factor. Continue dividing the numbers until you have a list of all of the prime factors.
Prime Number Factorization: Another way to find factors of a number is to use a list of prime numbers. A prime number is a number that is only divisible by itself and 1. To find factors of a number using a list of prime numbers, start with the smallest prime number. Then, see if the number is divisible by the prime number. If it is, write the prime number down as a factor of the number. Continue checking the number for divisibility by prime numbers until you have a list of all the factors of the number.

Example of Factorization

Let’s find the factors of the number 12.

Using a factor tree

12
/ \
6 2
/ \
3 2

The factor tree shows that the factors of 12 are 1, 2, 3, 4, 6, and 12.

Using a list of prime numbers

The prime factorization of 12 is 2 x 2 x 3. Therefore, the factors of 12 are 1, 2, 3, 4, 6, and 12.

How to Find Factors of a Number in a Montessori Way?

In this video lesson, we will be exploring the Montessori method of finding factors, which uses pegs and a board to visually see all possible combinations. This method is particularly helpful for children who are visual learners, as it helps them to understand the concept of factors better.

Materials Required for Finding Factors of a Number

The Montessori pegboard is a board with evenly spaced holes into which pegs can be inserted.
Pegs, which can be of different colors.

Prerequisites of Factors

A child must be introduced to the concept of

Addition, subtraction, multiplication, and division.
factorization, prime factorization, and fact families.

Find factors using pegboards

Follow the below steps:

Invite the child to the table with the Montessori math material pegs and boards and tell them, today, we will be learning how to find factors of a number with this.
Now ask them to choose the number they want to find the factors for. Let’s say 18.
Get the Montessori pegs and board ready. Start with one peg on the board, representing the number 1, and add 18 pegs of 1.
After that, add another peg representing the number 2 and alternate two pegs until 18 is substituted
Keep adding pegs in sequence until you reach the number you want to find the factors for.
Now, move the pegs around on the board to find different combinations that divide evenly into the original number. You can move the pegs horizontally, vertically, or diagonally.
Ask the child to count the number of pegs in each combination to determine the factors of the original number. The factors are the numbers that divide the original number evenly.

This method is a fun, and interactive way of developing the child’s logical thinking.

Activities Related to Finding Factors

Here are some activities related to finding factors in a Montessori way:

Use Montessori pegs and boards to find the factors of different numbers. Have the child choose a number and find all possible combinations of pegs that divide evenly into that number. You can also ask the child to find the factors of a specific number and see how many different combinations they can come up with.
Create a factorization chart using Montessori beads. This activity is best suited for older children who have already learned about prime numbers. To create the chart, choose a number and use Montessori beads to represent the number and its factors. For example, if you choose the number 12, you would use 1 bead, 2 beads, 3 beads, 4 beads, 6 beads, and 12 beads. Then, use different colored beads to represent the prime factors of each number. This activity helps children to visually see the relationship between different factors and prime numbers.
Play a game of factor bingo. Create bingo cards with different numbers on them and have the child cross off the factors of each number as they are called out. This game is a fun way to reinforce the concept of factors and help children to memorize them.

These activities can help children to better understand the concept of factors and make learning math more engaging and fun.

Watch the video to learn more about fact families and build a strong foundation in arithmetic to solve more complex problems.

How to Find Factors of a Number