If number A divided another number B exactly, we say that A is a factor of B. In this case, B is called a multiple of A.

B/A = X

Let’s consider following example

10/2 = 5

Then Factors of 10 are 2 X 5

Use following calculator for getting factors of number.

The H.C.F. of two or more than two numbers is the greatest number that divided each of them exactly.

There are two methods of finding the H.C.F. of a given set of numbers:

1. Factorization Method
2. Division method

Factorization Method:

Express the each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

Division Method:

Suppose we have to find the H.C.F. of two given numbers, divide the larger by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is required H.C.F.

The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

There are two methods of finding the L.C.M. of a given set of numbers:

1. Factorization Method
2. Division Method (Division Method is short cut method of LCM)

Factorization Method:

Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors.

Division Method:

Arrange the given numbers in a row in any order. Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.

LCM of two numbers can be calculated using following formula

$LCM (n1,n2) = \frac{n1 \times n2}{HCF(n1 ,n2)}$

LCM of 3 numbers can be calculated using following formula

LCM (A, B, C) = LCM [ LCM( A, B) , C]

Product of two numbers = Product of their H.C.F. and L.C.M

For Example

n1 X n2 = HCF (n1, n2) X LCM (n1, n2)

Following formulas are very helpful when solving HCF and LCM questions with fractions

$HCF = \frac{\mathrm{HCF} \mathrm{of} \mathrm{Numerator}}{\mathrm{LCM} \mathrm{of} \mathrm{Denominator}}$