Factoring Numbers In Math Fundamentals

>> Thursday, January 20, 2011

Introducing factors to kids in grade 4 to 5
Finding factors is introduced to kids in grade five (some schools do it in late grade four). To learn factoring, kids should be very good in times tables and they should know basic multiplication and division. Finding factors of a number is a basic math skill which enables students to deal with fractions, help kids to understand higher concepts in algebra, such as rational expressions or dividing polynomials.

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The key to learn factoring is to know prime and composite numbers. Students should know prime and composite numbers up to one hundred at least. This gives the idea for basic understanding of factoring.
First of all, students should know that what the factors are?
I tell my students that when a given number can be written as multiplication of other two numbers, then the other two numbers are called the factors of the given number.
For example; "2" can be written as "1 x 2 = 2", hence "2" have two factors, "1" and "2" itself.
Similarly, "6" can be written as "1 x 6 = 6" and also "2 x 3 = 6", hence "6" have four factors, 1, 2, 3, 6.
From above examples, it is clear that "number itself" and "one" are always the factor of a given number. From this we can define two kinds of numbers called prime and composite.
Prime numbers:
When a number has only two factors and which are " the number itself" and "one" then this is an example of a prime number. For example; numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 93, 97 are all the composite numbers from 1 to 100.
In other words, prime numbers are the those which can't be divided by any other number (except number one).
Composite numbers:
Once students got the prime numbers, they can understand the composite numbers easily. Composite numbers are those which have more than two factors. For example; 4, 6, 8, 9, 10 and so on are the composite numbers.
In other words, these numbers are those which can be divided by other numbers (other than one).
Once students are comfortable about prime and composite numbers, they can start factoring.
If the number is prime then these are the only factors. But if it is composite then there are more factors than two factors.
For example; let's find all the factors of 32.
There is no other factor which can divide 32. Similarly students can write all the factors of any other numbers.

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