We will discuss here about multiples and factors and how they are related to each other.

Factors:

Factors of a number are those numbers which can divide the number exactly.

For example, 1, 2, 3 and 6 are factors of 6. 1, 2 and 4 are factors of 4.

(i) 1 is the factor of any number.

(ii) Any number is factor of itself.

(iii) 0 has infinite factors. In fact all numbers are factors of zero.

(iv) 0 is not factor of any number because division by 0 is meaningless.

**Every number has a fixed number of factors.**

**For example:**

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

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

Multiples:

A number is called multiple of another if it is exactly divisible by the other number.

For example, 8 is a multiple of 4. 6 is multiple of 3. Multiple of any numbers are infinite.

We know counting numbers they are 1, 2, 3, 4, 5, 6, ...... To get multiples of any number, we multiply counting numbers with that number. For example, to get the list multiples of 3 we need to multiply counting numbers with 3 i.e., 1 × 3 = 3, 2 × 3 = 6, 3 × 3 = 9, 4 × 3 = 12, 5 × 3 = 15 and so on. So, the multiples of 3 are 3, 6, 9, 12, 15 and so on.

**Multiples of any numbers are unlimited.****For example:**

Multiples of 2 are 2, 4, 6, 8, 10, 12, 14 etc.

Multiples of 5 are 5, 10, 15, 20, 25, 30 etc.

Multiples of 11 are 11, 22, 33, 44, 55, 66 etc.

Multiples of 8 are 8, 16, 24, 32, 40, 48 etc.

Multiples of 14 are 14, 28, 42, 56, 70, 84 etc.

From the above explanation we understand that **how multiples
and factors are related to each other**.

Suppose for example, 12 = 1 × 12, 12 = 2 × 6, 12 = 3 × 4; this shows that each of the number, i.e., 1, 2, 3, 4, 6 and 12 are factors of 12.

In other words, we can say that 12 is a multiple of each one of the numbers 1, 2, 3, 4, 6 and 12.

Thus, when a divisor divides a number and there is zero remainder, then the divisor is called the factor of the dividend and dividend is called the multiple of the divisor.

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