Factors: An Important Concept in Mathematics

Definition of Factor

When a given number can be divided by another number, including itself, without any remainder, it is called a factor of the given number.

Let’s explain factors through an example:

Suppose there is a number 6 and we have to find out its factor

Condition for factor: Numbers that can divide the number 6 without leaving a remainder.

1. 6/1 = 6 (6 is divided by number 1 without leaving remainder; therefore, number 1 is called factor of 6.)
2. 6/2 = 3 (6 is divided by number 2 without leaving remainder; therefore, number 2 is called factor of 6.)
3. 6/3 = 2 (6 is divided by number 3 without leaving remainder; therefore, number 3 is called factor of 6.)
4. 6/4= 1.5 (6 is divided by number 4 with remainder; therefore, number 4 is not a factor of 6)
5. 6/5 = 1.2 (6 is divided by number 5 with remainder; therefore, number 5 is not a factor of 6)
6. 6/6 = 1 (6 is divided by number 6 without leaving remainder; therefore, number 6 is called factor of 6.)

Based on the information above, Number 6 can be divided evenly by 1, 2, 3, and 6 . Therefore,

Factor of Number 6 = ( 1, 2, 3, 6)

Let’s take another example: Find the factors of number 24

Condition for factor : Numbers that can divide the number 24 without leaving a remainder.

The number 24 can be fully divided by 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore, Factors of Number 24 = ( 1, 2, 3, 4, 6, 8, 12, 24 )

Greatest or Highest Factor

From the above two examples, we can conclude that the greatest factor of a number is the number itself.

Least Factor

A “least factor” is the lowest positive integer that divides a given number without leaving a remainder . Since 1 is the smallest positive integer and a factor of all positive integers, it is always the least factor.

Prime Factor

Every number is divisible by 1 and itself. Therefore, we can say that each number has at least two factors: 1 and the number itself. When a number has only these two factors, it is called a Prime Factor. Prime factors are factors that are prime numbers.

Composite Factor

A number that has more than two factors is called a composite number.

Factor Pair

Factors come in pairs. If ‘a’ is a factor of ‘b,’ then ‘b/a’ is also a factor of ‘b.’ For example, if 2 is a factor of 12, then 6 is also a factor of 12.

Important Facts about Factors

Factors of any number are finite.

Multiple-Choice Questions on Factor :

Here are some multiple-choice questions (MCQs) on factors:

1. What is a factor of a number?

A) A number that is divisible by the given number.

B) A number that can divide another number without leaving a remainder.

C) A number that is larger than the given number.

D) A number that is a multiple of the given number.

2. Which of the following numbers is a factor of 24?

   A) 5

   B) 12

   C) 17

   D) 30

3. What are the factors of 18?

   A) 2 and 9

   B) 3 and 6

   C) 4 and 5

   D) 7 and 8

4. What is the smallest prime factor of 21?

   A) 1

   B) 2

   C) 3

   D) 5

5. If a number has exactly two factors, what type of number is it?

   A) Prime number

   B) Composite number

   C) Odd number

   D) Even number

6. What is the greatest factor of 24?

   A) 2

   B) 6

   C) 24

   D) 3

7. How many factors does the number 1 have?

   A) 0

   B) 1

   C) 2

   D) Infinite

8. Which of the following numbers has the most factors?

   A) 6

   B) 8

   C) 10

   D) 12

9. What is the product of all the prime factors of 36?

   A) 6

   B) 9

   C) 18

   D) 36

10. If a number has factors 1, 2, 4, 5, 10, and 20, what is the number?

    A) 10

    B) 20

    C) 40

    D) 50

Answers:

1. B) A number that can divide another number without leaving a remainder.

2. B) 12

3. B) 3 and 6

4. C) 3

5. A) Prime number

6. C) 24

7. B) 1

8. D) 12

9. D) 36

10. D) 50