Chapters

Like other types of number, composite numbers also holds importance in Maths. The easiest definition of a composite number is a number that has more than two divisors. Yes, composite numbers are the opposite of prime numbers because the condition of the prime number is that it should have only two divisors (which are 1 and itself) while composite number says that it should have more than two divisors. For example, our objective is to find whether the number 14 is a prime number or composite number? The best way to find whether this is a composite number or not is to divide it by prime numbers which are lesser than 14 (because in this example, we are using 14). If the remainder is a perfect whole number that means a number is a composite number otherwise it will be a prime number. We all know 2 is a prime number, let's divide 14 by 2. When we divide 14 by 2, the quotient will be 7 and the remainder will be 0. Although, you can go further on like divide 14 by 3, 5, 7, 11 but it is not necessary because the above division is enough to declare that 14 is a composite number. Here is another example, find whether 7 is a prime or composite number. Now we will divide 7 by all the prime numbers below 7.

\frac { 7 }{ 2 }; remainder = 1,

\frac { 7 }{ 3 }; remainder = 1,

\frac { 7 }{ 5 }; remainder = 2.

Hence, we can conclude that 7 is a prime number, not a composite number. Composite numbers can be expressed as products of powers of prime numbers. Such an expression is called the decomposition of a number in prime factors. For example, decompose 70 into its prime factors.

The first step is to divide the number by 2 (which is the first prime number). Divide the number until the quotient becomes a decimal number. Don't add that decimal number in your division list because that is just an indication.

\begin{matrix} 2 \\ \\ \\ \end{matrix}\begin{vmatrix} 70 \\ 35 \\ \\ \end{vmatrix}

After that, divide the remaining number by 3 (because it is the next prime number after 2) but when we divide 35 by 3, it doesn't give quotient as a whole number that is why we will jump to the next prime number(which is 5):

\begin{matrix} 2 \\ 5 \\ \\ \end{matrix}\begin{vmatrix} 70 \\ 35 \\ 7 \\ \end{vmatrix}

Keep repeat the above step again until you get 1:

\begin{matrix} 2 \\ 5 \\ 7 \\ \end{matrix}\begin{vmatrix} 70 \\ 35 \\ 7 \\ 1 \end{vmatrix}

70 = 2 \times 5 \ times 7

Factoring

To factor a number or to decompose it into factors, carry successive divisions out between its prime divisors.

To make the divisions, use a vertical bar, to the right write the prime divisors and to the left the quotients.

Example

Q. Find the factors of 432.

\begin{matrix} 2 \\ 2 \\ 2 \\ 2 \\ 3 \\ 3 \\ 3 \\ \end{matrix}\begin{vmatrix} 432 \\ 216 \\ 108 \\ 54 \\ 27 \\ 9 \\ 3 \\ 1 \end{vmatrix}

432 = { 2 }^{ 4 } \times { 3 }^{ 3 }

Do you need to find a Maths tutor?

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars 5.00/5 - 1 vote(s)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.