H.C.F & L.C.M of numbers

H.C.F & L.C.M of numbers

Factors and multiples:

If a number A  divides another number B exactly we say that  A is a factor of B.

HIGHEST COMMON FACTOR (H.C.F) or GREATEST COMMON FACTOR (G.C.F)

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

H.C.F can be solved by 2 methods .

Method1: factorization method

Method 2 : division method

Easiest and fastest method to solve H.C.F problems is division method

Example: Find HCF of 513, 1134, 1215

                  First choose biggest of these numbers here 1215 is highest so now divide 1215 with next highest 1134

                 1134) 1214(1

                             1134

                                 81)1134(14

                                            81

                                         324

                                         324

                                            0

HCF of 1134, 1214 is 81

Now divide 513 with 81

                          81)513(6

                                486

                                  27)81(3

                                        81

                                         0                  

Therefore the HCF of 513, 1134, 1215 is 27

LCM of numbers:

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

Shortcut method to find lcm of given numbers is common division method.

Example: Find LCM of 16,24,36,54

2	16 – 24 – 36 – 54
2	8 – 12 – 18 – 27
2	4  -   6   -  9 – 27
3	2   -  3  -   9 – 27
3	2   -  1  -  3  -  9

                            2   -  1  -   1 -   3

 LCM =2*2*2*3*3*2*3=432

Product of 2 numbers = Product of HCF and LCM

Co –primes: Two numbers are said to be co-prime if their HCF is 1

HCF AND LCM OF FRACTIONS:

1.    HCF = HCF of Numerators

                             LCM of Denominators

2.    LCM = LCM of Numerators

                              HCF of Denominators