How many of you are still in doubt what factors mean? It is quite obvious that a lot of you actually don’t understand the way your teacher has taught you. No worry! You can simply go through this chapter and get your fundamentals cleared! We will discuss all the factors of numbers in this chapter.

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## Factors of a Number

To get a product, a number can be multiplied. These numbers are **factors** of the product. By multiplying the number by the natural number **Multiples** of a number are obtained.

Example:

- 5×2=10
- 6×2=12
- 7×2=14
- 8×2=16 and so one.

Therefore 10,12,14,16 these numbers are the multiples of 2. Multiples of 4:

1^{st} |
2^{nd} |
3^{rd} |
4^{th} |
5^{th} |
6^{th} |
7^{th} |
8^{th} |
9^{th} |
10^{th} |

4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |

**Let us look at some more examples of factors.**

In the following example, let us assume that each group should have an equal number of apples. No Apple should be left out of the box but each grouping should be different. In one box we have 12 apples. So, here 1×12= 12. Now, we decide to divide the apples equally into 2 boxes. So, we can put 6 apples in two boxes each.

Now, 2×6=12. If we further decide to put the 12 apples equally in 3 boxes, we put 4 apples in each of the 3 boxes. Here 3×4 = 12. Here we arranged 12 apples in 3 different groups having 12, 6. 4 apples each. So we are able to know that 1, 2, 3, 4 … are the factors of 12.

- When a number is divided by one of its factors then there is no remainder and remember this key point also in order to find the factors of a number, we divide the number by 1, 2, 3, 4, …

**Multiples**

We know that 3×4=12 and that 12 here is a product of 3 and 4 and is also one of the multiples of 3,4.

- Multiples of 3: 3, 6, 9, 12, 15, 18…..
- Multiples of 4: 4, 8, 12, 16, 20, 24….

Let us take another example: 2×3×5=30 is the product of 2, 3, and 5 and also one of the multiples of 2, 3, and 5.

- Multiples of 2: _, _, _, 24, 26, 28, 30, _, _
- The multiples of 3: _, _, _, 21, 24, 27, 30, _, _
- Multiples of 5:_, _, _, 15, 20, 25, 30, _, _

## Even and Odd Numbers

Even Numbers | Odd Numbers |

Those numbers which are multiples of 2 is known as even numbers.
Ex : 2, 4, 6, 8, 10 … |
Those numbers which are not multiples of 2 is known as odd numbers.
Ex: 1,3, 5, 7, 9…. |

### Highest Common Factor

From the common factors of given two numbers who is the greatest or the highest factor among them that is known as Highest Common Factor (HCF).

### Lowest Common Factor

From two or more numbers smallest number which is the multiple of each of the numbers is known as a lowest common factor (LCM).

### Prime Factorisation

Prime Factorisation is defined as factorization in which every factor is prime.

## Solved Example For You

Q. By prime factorization method, calculate the LCM and HCF of 264 & 624.

Ans: The factors of given numbers are 264=2×2×3×11 & 624= 2×2×2×2×3×11. Then select the factors which are common for both the numbers. That is 2×2×2×3. By multiplying the common factors we can get HCF that is 2 × 2 × 2 × 3 = 24. But for LCM multiply the remaining factors like 2×2×2×3×2×11×13 = 6864. So 6864 is the LCM for 264, 624.

Q. What do you mean by factors of a number?

Ans: To get a product number can be multiplied. These numbers are called Factors of the product. By multiplying the number by the natural number Multiples of a number are obtained.

Q.What is a highest common factor?

Ans: From the common factors of given two numbers who is the greatest or the highest factor among them that is known as Highest Common Factor (HCF).

Ques. What is an odd number?

Ans. The odd numbers are the whole numbers which are not divisible into pairs. When the odd numbers are divided by 2 then they leave a remainder of 1. Odd numbers have some digits such as 1, 3, 5, 7 or 9 in their one’s place. Numbers like 1, 3, 5, 7, 9, 11, 13, and 15 and so on are the sequential odd numbers.

Ques. Is there an end to numbers?

Ans. The answer is no, there is no end to the numbers. The numbers just keep on going. Sometimes the people form the mathematics subject say that the number goes to infinity. This statement just means that the counting of the numbers does not have any limit.

Ques. Which numbers are used in the binary code?

Ans. In the mathematics subject and in the digital electronics as well, a binary number is a number that is expressed in the base-2 number system or in the binary number system. These systems use only 2 symbols that are ‘0’ and ‘1’.

Ques. Are numbers really infinite?

Ans. The word Infinity is not any number. Infinity is the name of a concept. The mathematicians divide the infinity sets into 2 different groups. These 2 groups are the countable and uncountable sets

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