Factors and Multiples

If one number x is exactly divisible by another number y, then x is multiple of y and y is the factor of x

A factor of a number is an exact divisor of that number.

Example: 5 exactly divides 30. 5 is a factor of 30 and 30 is multiple of 5

Answer the following

List the multiples of 3 between 1 and 20

3	x	1	=	3
3	x	2	=	6
3	x	3	=	9
3	x	4	=	12
3	x	5	=	15
3	x	6	=	18
3	x	7	=	21
3	x	8	=	24
3	x	9	=	27
3	x	10	=	30

Multiplication table of 3

In the above Table, multiples of 3 between 1 and 20 is 3, 6, 9, 12, 15, 18.

2. What are factors of 15

1x15=15
3x5= 15
So 1, 3, 5, 15 are factors of 15

Answer the Following

1. Find the multiples of 7 below 100

2. Find the multiples of 9 below 100

3. Find the common multiples of 7 and 9 below 100

4. Find the least common multiple of 9 and 7

By finding the multiples of different numbers, we can find the common multiples of those numbers. Then find LEAST COMMON MULTIPLE (LCM)

From the questions 3 and 4 above,

9-> 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,99

7-> 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98. in these common multiple is 63. That is least common multiple. Here we are listing out numbers and finding the common multiple. But we cannot list all multiples every time.

Finding factors of number

1. Find all factors of 24

1 x 24 = 24

2 x 12 = 24

3 x 8 = 24

4 x 6 = 24

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

2. Find all factors of 64

1 x 64 = 64

2 x 32 = 64

4 x 16 = 64

8 x 8 = 64

Factors of 64 are 1, 2, 4, 8, 16, 32, 64

Take any multiplication sentence, for example, 5 x 6 = 30. Here, 5 and 6 are factors of 30
1 x 30 = 30
2 x 15 = 30
3 x 10 = 30
5 x 6  = 30
Above the multiplication sentences, the product is 30. Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. Let  us see a few more examples.

Factors of 42	Factors of 64
1 x 42 = 42	1 x 64 = 64
2 x 21 = 42	2 x 32 = 64
3 x 14 = 42	4 x 16 = 64
6 x 7 = 42	8 x 8 = 64

Factors of 42 Factors of 64

1, 2, 3, 6, 7, 14, 21, 42 1, 2, 4, 8, 16, 32, 64

Highest Common factor(HCF) or Greatest Common factor(GCF)

HCF and GCF are the same but different terms to find greatest common factor of two or more numbers. 
Factors of 42 = 1, 2, 3, 6, 14, 21, 42
Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Common factors of 42 and 64.
Common factors of 42 and 64 are 1 and 2, the highest factor is 2.
HCF or GCF of 42 and 64 is 2.

The above given examples, factors are listed. But we cannot list all factors when we find common factors for higher numbers.

We can use two other methods to find the factor tree method and the division method. These methods are used for PRIME FACTORIZATION