common factor

[latexpage]
H.C.F- The highest common factor of two or more given number is the highest (or greatest) of their common factor.
e.g. 24 = 1,2,3,4,6,8,12,24
36 = 1,2,3,4,6,9,12,36
H.C.F = 6

Method Factorization:
factor of 18
factor-of-48

$18=\underline{2*3}*3$
$48=2*2*2*\underline{2*3}$
$HCF=2*3=6$

Euclid’s Algorithm
determining the HCF of 18 & 30.
Euclide12 16 20
Multiple of 6 are 12 18 24
So LCM of 4 and 6 are 12

Method factorization
method-factorization

So $LCM =3x3x3x3=81$

The product of the H.C.F & L.C.M of two numbers is equal to the product of the number.
Example:
Given number 16 and 24.
their $HCF=8$ and $LCM=48$
then $16*24=8*48=348$

Absolute value of integer |-5| = 5, but -|5| = 5, |+5| = 5