Factorisation for Dummies
noun
What does Factorisation really mean?
Factorisation is a mathematical term that might sound a little fancy, but let me assure you, it's not as complicated as it may seem. It's actually a pretty useful concept that helps us break down numbers or expressions into smaller pieces, just like how we take apart a puzzle. When we factorize, we're essentially finding the factors, or the numbers that can multiply together to give us the original number or expression.
Think of factorisation like breaking down a big chocolate bar into smaller pieces. Let's say we have a big chocolate bar with 12 squares. We can factorize it by finding the factors of 12, which are 1, 2, 3, 4, 6, and 12. These numbers can be multiplied together to give us 12. So, we can break the chocolate bar into smaller pieces, like having 1 piece, 2 pieces, 3 pieces, and so on, or even all 12 pieces at once.
But factorisation doesn't only work with numbers, it can also be used with algebraic expressions. In this case, we look for common factors that can be taken out from each term of the expression. Let's say we have the expression 2x + 4x. We notice that both terms have a common factor, which is x. So, we can factorize this expression as x(2 + 4), which simplifies to 6x.
Now, there's another aspect of factorisation called prime factorisation. Prime numbers are numbers that can only be divided by 1 and themselves without having any remainders. When we perform prime factorisation, we break down a number into its prime factors, which are the smallest prime numbers that can multiply together to give us the original number.
Let's take the number 24 as an example. We can start by dividing it by the smallest prime number, which is 2. So, we have 24 ÷ 2 = 12. Now, we divide 12 by 2 again, giving us 12 ÷ 2 = 6. Finally, we divide 6 by 2 once more, giving us 6 ÷ 2 = 3. Now, we can't divide 3 any further because it's a prime number. So, the prime factorisation of 24 is 2 × 2 × 2 × 3, which can also be written as 2^3 × 3.
In conclusion, factorisation is the process of breaking down numbers or algebraic expressions into smaller factors. It helps us understand the building blocks that make up a number or an expression, making it easier to work with and solve mathematical problems. So, just like taking apart a puzzle or breaking down a chocolate bar into smaller pieces, factorisation helps us simplify and understand the underlying structure of numbers and expressions.
Think of factorisation like breaking down a big chocolate bar into smaller pieces. Let's say we have a big chocolate bar with 12 squares. We can factorize it by finding the factors of 12, which are 1, 2, 3, 4, 6, and 12. These numbers can be multiplied together to give us 12. So, we can break the chocolate bar into smaller pieces, like having 1 piece, 2 pieces, 3 pieces, and so on, or even all 12 pieces at once.
But factorisation doesn't only work with numbers, it can also be used with algebraic expressions. In this case, we look for common factors that can be taken out from each term of the expression. Let's say we have the expression 2x + 4x. We notice that both terms have a common factor, which is x. So, we can factorize this expression as x(2 + 4), which simplifies to 6x.
Now, there's another aspect of factorisation called prime factorisation. Prime numbers are numbers that can only be divided by 1 and themselves without having any remainders. When we perform prime factorisation, we break down a number into its prime factors, which are the smallest prime numbers that can multiply together to give us the original number.
Let's take the number 24 as an example. We can start by dividing it by the smallest prime number, which is 2. So, we have 24 ÷ 2 = 12. Now, we divide 12 by 2 again, giving us 12 ÷ 2 = 6. Finally, we divide 6 by 2 once more, giving us 6 ÷ 2 = 3. Now, we can't divide 3 any further because it's a prime number. So, the prime factorisation of 24 is 2 × 2 × 2 × 3, which can also be written as 2^3 × 3.
In conclusion, factorisation is the process of breaking down numbers or algebraic expressions into smaller factors. It helps us understand the building blocks that make up a number or an expression, making it easier to work with and solve mathematical problems. So, just like taking apart a puzzle or breaking down a chocolate bar into smaller pieces, factorisation helps us simplify and understand the underlying structure of numbers and expressions.
Revised and Fact checked by Sarah Anderson on 2023-11-05 20:10:51
Factorisation In a sentece
Learn how to use Factorisation inside a sentece
- Factorisation is like breaking a number into smaller pieces. For example, if we factorise the number 12, we can write it as 2 multiplied by 6, or as 3 multiplied by 4.
- Factorisation can also be useful in solving equations. For instance, if we have the equation x^2 - 9 = 0, we can factorise it as (x - 3)(x + 3) = 0 to find the values of x.
- When we factorise a polynomial expression, we look for common factors among its terms. For example, in the expression 2x^2 + 4x, we can factorise it as 2x(x + 2), where 2x is the common factor.
- In geometry, we can use factorisation to find the dimensions of rectangular shapes. If the area of a rectangle is given as 24 square units, and one of its sides is 3 units, we can factorise 24 as 3 multiplied by 8 to find the other side.
- Factorisation is also used in finding the prime factors of a number. For instance, the prime factorisation of the number 18 is 2 multiplied by 3 squared.
Factorisation Synonyms
Words that can be interchanged for the original word in the same context.
Factorisation Hypernyms
Words that are more generic than the original word.
Factorisation Category
The domain category to which the original word belongs.