TUTORIAL

Factor

A factor may be defined as a number or an expression that divides another number or expression evenly.

Multiple

A multiple of a number is that number multiplied by an integer.

For example, if a number ‘x’ divides the other number ‘y’, then ‘x’ is the factor of ‘y’ and ‘y’ is the multiple of ‘x’.

HCF

HCF is Highest Common Factor. It may be defined as the greatest number that divides both numbers equally.

For example, HCF of 20 & 40 is 20.

HCF between two(or more) numbers, can be evaluated using two methods :

1. Prime Factorization
2. Division Method

In Prime Factorization method, numbers are expressed in the terms of the product of their prime factors. The product of least powers of common prime numbers gives HCF.

Like, HCF of 20 & 40 :

20 : 2² * 5¹

40 : 2³ * 5¹

So, common power : 2² * 5¹

LCM

LCM is Least Common Multiple. It may be defined as the least number that can be divided by each one of the numbers.

For example, LCM of 20 & 40 is 40.

LCM between two(or more) numbers, can be evaluated using two methods :

1. Prime Factorization
2. Division Method

In Prime Factorization method, numbers are expressed in the terms of the product of their prime factors. The product of highest powers of all the factors gives LCM.

Like, LCM of 20 & 40 :

20 : 2² * 5¹

40 : 2³ * 5¹

So, common power : 2³ * 5¹ = 40

Relationship between HCF & LCM

[math]
\boxed
{
HCF \;=\; \frac{Product\; of \;two \;Numbers}{LCM}
}
[/math]