### FACTOR

**A** **factor** of a given number is every number that **divides exactly ** into that number**.**

### Example

Write down all factors of 10.

10 = 2 x 5, so numbers 2 and 5 are factors of 10.

Also 10 = 10 x 1, so 10 and 1 are factors of 10.

The factors of 10 are 1, 2, 5, 10.

**NOTE**: Number **1** and the **number itself** are always factors of any number.

### PRIME AND COMPOSITE NUMBERS.

A **prime number** has exactly **2 factors**, the number **itself** and ** 1**.

In other words, the prime number can be divided only by 1 and by itself.

**NOTE:** **0** and **1 **are **not** prime numbers.

Example: 5 is a prime number, because the only factors it has are 1 and 5.

The prime numbers less than 20 are **2,3,5,7,11,13,17,19**

#### Example:

Find all prime factors of 30.

Solution:

All the factors of 30 are 30, 15, 10, 6, 5, 3, 2, 1

But only 5, 3 and 2 are prime numbers.

Thefore all prime factors of 30 are 2, 3 and 5.

A** composite number ** has ** at least one more factor ** that the number itself or 1.

In fact, all whole numbers that are not prime are composite **except **for **1** and **0,** which are not prime and not composite.

The composite numbers less than 20 are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

**DIVISIBILITY RULES**

The simple divisibility rules will help you to find factors of a number.

For rest go to CAT India Online’s CATclub

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