Concise Mathematics Class 6 ICSE Solutions for Chapter 9 - Playing with Numbers

The concept of the number of a number can be explained as the order of its factors. As in the case of an ordinary number we could say the number of 5 is 10 (or 5,10). However, when it comes to prime numbers the concept of the number of the number cannot be explained by simple explanation.

In order to understand the prime factorization of numbers, we would have to introduce a few concepts which we had already discussed in one of the previous chapters. However, before we take a step further we have to clear a few things which are going to come in the way of our understanding. The following few paragraphs will be a short explanation of some basics of prime factorization, prime number theory, number theory, and simple prime factors.

A number of a number may seem like a simple concept to understand but it’s actually quite a complex one. The simple explanation is that in order to number the number you must divide the number into two sets. The set which contains all the factors of the number in it. Let’s see an example to make it a little clearer.

Consider a number 8 =2*2*2. We know that 2 is the smallest number in the set which contains all the factors of 8 in it. This set is made up of 2,4,8.

However, the number 3 =3*3 is not in the set as it is not divisible by 3. Since a number is divisible by 3 if its highest power of 3 is greater than 1 we would say that 3 is the odd number. That is a number which cannot be written as a multiple of 3. However, in order to count the number we cannot ignore 3 as we have to count 3.

It can also be expressed as the product of all the factors of the number. Let’s see an example.

3 is the number of number 25 =5*5*5

The set of factors of the number 25 =5*5*5 can be expressed as 5,10,25

The set of factors of the number 25 =5*5*5 is made up of 5,10,25

Thus, 25 is the number because of the products of all the factors of 25 =5*5*5

Note: The numbers we discussed in this section will only be the prime factors and not the composite factors which you can find out from the factorization rule. A composite number is any number which has factors other than 1 or it can be also said as an integer which cannot be divided into prime factors.

Prime Factor of a Number

All the prime factors of the number are also called the prime factorization. A number can be represented in many ways to show the prime factors.

It’s not necessary that all the prime factors are put in the form of a product of their prime factors but it is not considered to be wrong. The most common way to write the prime factorization is to use the product sign “*”.

Let’s get started with the prime factors of numbers!

Numbers, What do We Mean by ‘Number’?

The number is anything which has no beginning and no ending. In mathematics, we say that a number is the whole unit which can not be broken down into smaller units. Number is a unit of measurement. Anything can be represented as a number, for example, we can say that 2*3 is a number because there is no zero (which is the base) so that 2 times 3 is a number but it is just one unit so it can not be broken down into smaller units and hence it is a number. The number is the set of digits that the number consists of.

Any number can be represented as a number sequence. The sequence is the set of numbers that we enter to get the desired number. For example, if we want to represent the number 1, we can represent the number 1 by entering digits in the order 1,2,3,4,5,6,7,8,9,0

A number can be represented by anyway to make the digit of the number sequence in a non-decimal way. There are many ways to do this.

If the number is written as a decimal, we write it as a sequence of 0,1,2,3,4,5,6,7,8,9. But sometimes it is required to represent the number in a different way like in English, it is written as 123456.