Learn Everything About Factors and Multiples | From Basics to Advanced Learning | Quiznest.in

1. Introduction to Factors and Multiples:

1.1

Factors are like the building blocks of a number. When you multiply these factors together, you get the original number. For example: Factors of 6 are 1, 2, 3, and 6 because 1 x 6 = 6 and 2 x 3 = 6.

1.2

For example: Factors of 8 are 1, 2, 4, and 8 because 1 x 8 = 8, 2 x 4 = 8. Also, factors of 12 are 1, 2, 3, 4, 6, and 12 because 1 x 12 = 12, 2 x 6 = 12, 3 x 4 = 12.

1.3

Also, factors of 9 are 1, 3, and 9 because 1 x 9 = 9 and 3 x 3 = 9. Factors of 15 are 1, 3, 5, and 15 because 1 x 15 = 15 and 3 x 5 = 15.

1.4

So, now we know, factors are the numbers that can be multiplied together to get a certain number. Every whole number has at least two factors: 1 and itself.

1.5

Multiples are the result of multiplying a given number by another whole number. For instance, the multiples of 5 are 5, 10, 15, 20, and so on because each of these numbers can be obtained by multiplying 5 by 1, 2, 3, 4, etc.

1.6

Multiples go in the opposite direction of factors; they are the numbers you get when you keep adding the original number.

1.7

For example: The multiples of 4 are 4, 8, 12, 16, 20, and so on. These numbers are obtained by multiplying 4 by 1, 2, 3, 4, 5, etc. The multiples of 7 are 7, 14, 21, 28, 35, and so on. These numbers are obtained by multiplying 7 by 1, 2, 3, 4, 5, etc.

1.8

For example: The multiples of 10 are 10, 20, 30, 40, 50, and so on. These numbers are obtained by multiplying 10 by 1, 2, 3, 4, 5, etc. In each case, you can see that the numbers listed are obtained by continuously adding the original number (4, 7, or 10) to itself.

2. Understanding Factors and Multiples Better:

2.1

Is 7 a factor of 35? Yes, because 7 divides 35 exactly with the remainder as 0. Thus, 7 is a factor of 35.

2.2

Is 11 a factor of 45? No, because 11 does not divide 45 exactly, leaving the remainder 1. Thus, 11 is not a factor of 45.

2.3

Is 4 a factor of 1728? Yes, because 4 divides 1728 exactly with the remainder as 0. Thus, 4 is a factor of 1728.

2.4

List all factors of 14. Answer: 1, 2, 7, 14 are all the factors of 14.

2.5

List first 3 non-zero multiples of 14. Answer: 14 x 1 = 14, 14 x 2 = 28, 14 x 3 = 42. Thus, 14, 28, 42 are the first 3 non-zero multiples of 14.

3. Properties of Factors and Multiples:

3.1

Properties of Multiples: 0 is a multiple of every number. For example, 25 x 0 = 0, 34 x 0 = 0. In regular usage, 0 is not expressed as the first multiple.

3.2

Properties of Multiples: The smallest multiple of 7 is 7 as 7 x 1 = 7. Multiples of a number are infinite as they carry on and on. Multiples of 10 are 10, 20, 30, 40, 50, 60, ...

3.3

Properties of Multiples: Every number is a multiple of 1. Example: 1 x 12 = 12. So, 12 is a multiple of 1 and 12. Every number is a multiple of itself. Example: 4 x 1 = 4. So, 4 is a multiple of 4 and 1.

3.4

Properties of Factors: 1 is a factor of each number, because 1 can divide every number exactly. Also, 1 is the only number which has only one factor.

3.5

Properties of Factors: What is the smallest factor? 1 is the smallest factor. What is the greatest factor? The number itself is the greatest factor. For example: 7 is the greatest factor of 7.