Posted by: catindiaonline | October 25, 2008

CAT Quant: HCF & LCM

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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