Concept -1

HCF → An HCF is a greatest number that divides a series of given numbers exactly.

It stands for highest common factor.

Methods of finding HCF

(a) Breaking into prime factors : - In this method the given numbers are broken into prime numbers. and common from both is taken.

Example → Find HCF of 15 and 35.

Step-I → Break into prime factors.

15 = 3 × 5

35 = 5 × 7

Step -II → Pick up the common multiplicant from both numbers.

So HCF = 5

(b) Methods of division → In this method we divide the greater number by smaller number. and Repeat the procedure by dividing the divisor by remainder.

Process continues till we obtain a zero remainder.

Example → Find HCF of 56 and 70

Step-I →  

             table row cell 56 right parenthesis 70 left parenthesis 1 end cell row cell space table row cell bottom enclose 56 end cell row cell space space space space space space space space 14 right parenthesis 56 left parenthesis 4 end cell row cell space space space space space space space space space space bottom enclose 56 end cell row cell space space space space space space space space space space bottom enclose space 0 space end enclose end cell end table end cell end table

The Last divisor term will be H.C.F. of numbers. So H.C.F. = 14.

Note → Finding the HCF of more than two numbers by method of division.

Step -I → Find H.C.F. of any two numbers.

Step -II → Then find H.C.F. of H.C.F. and 3rd number. this HCF would be final H.C.F.

Example → Find H.C.F. of 191, 573, 1337

Step-I → Find H.C.F. of 573 and 1337

              begin mathsize 14px style table row cell 573 right parenthesis 1337 left parenthesis 2 end cell row cell space table row cell bottom enclose 1146 end cell row cell space space space space space space space space 191 right parenthesis 573 left parenthesis 3 end cell row cell space space space space space space space space space space bottom enclose 573 end cell row cell space space space space space space space space space space bottom enclose space 0 space end enclose end cell end table end cell end table end style

So 191 is the H.C.F.

Now H.C. F. of 191 and 191 would be = 191.

So H.C.F. of 191

Finding HCF of decimals → Convert them in whole quantity and find H.C.F. of them by above rules.

HCF of fraction → fraction is defined as  = Numerator over demoninator

H.C.F. of fractions = fraction numerator straight H. straight C. straight F space of space Numerator over denominator LCM space of space denominator end fraction

Example → Find HCF of begin mathsize 14px style 2 over 3 and space 3 over 2 end style

H.C.F. = fraction numerator HCF space of space left parenthesis 2 comma space 3 right parenthesis over denominator LCM space of space left parenthesis 3 comma space 2 right parenthesis end fraction equals 1 over 6 Ans.

Concept-II → LCM

  • LCM stands for "Least common multiple"
  • It is the least number which is exactly divisible by both or all given numbers.
  • Method of finding LCM

Method of prime factors:-

Step-I → Break the number into prime factors.

Step-II → Select the common factors of both the numbers.

Step-III → Then select the remaining factors

Step -IV → Multiply them.

Example → Find LCM of 42 and 70.

42 = 2 × 3 × 7

70 = 2 × 5 × 7

LCM = 2 × 7 × 3 × 5 = 210

LCM of fractionsfraction numerator LCM space of space Numerator over denominator LCM space of space denominator end fraction

Example → Find LCM of 1 half space and space 3 over 8

fraction numerator LCM space of space left parenthesis 1 comma space 3 right parenthesis over denominator HCF space of space left parenthesis 2 comma space 8 right parenthesis end fraction equals 3 over 2

Some important formulae.

(a)  LCM × HCF = first number × second number.

(b) If a number is divided by a, b and c. and leaves remainder 'k' in each case then the number would be 

LCM of (a, b, c) + K

(c) On dividing a number by 'a', 'b' and 'c' if we get a-k, b-k, and c-k as remainder respectively then that number will be

L.C.M. of (a, b, c) – k.

(d) If a number, after adding 'k' ,is exactly divisible by 'a', 'b' and 'c' then the number will be

L.C.M. of (a, b, c) – k

  • Test 1

    15 Questions
    15 Minutes
    70% Complete
    0%
  • Test 2

    10 Questions
    15 Minutes
    70% Complete
    0%
  • Test 3

    10 Questions
    15 Minutes
    70% Complete
    0%
  • Test 4

    10 Questions
    15 Minutes
    70% Complete
    0%
  • Test 5

    10 Questions
    15 Minutes
    70% Complete
    0%
  • Test 6

    10 Questions
    15 Minutes
    70% Complete
    0%
  • Test 7

    10 Questions
    15 Minutes
    70% Complete
    0%