Factor : A number is said to be a factor of another number it divides the other
E.g. 2 and 3 are factors of 6.
Common Factor : A common Factor of two or more numbers is a number that
divides each of them exactly. E.g. 3 is a common factor of 9, 15, 21, 36.
Highest Common Factor (HCF) : HCF of two or more numbers is the greatest
factor which divides each of them exactly. E.g. 12 is the HCF of 24 and 36.
Note : Greatest Common Measure is the another name for Highest Common
Methods of Finding HCF
Prime Factorization method : First of all the numbers are broken into prime
factors and then all the common factors of all the numbers are multiplied to get
Q Find the HCF of 42, 70 and 126.
Division Method – The greater is divided by the smaller number, then the
divisor is divided by the remainder, then the remainder is divided by the next
remainder and the process continues until no remainder is left. The last divisor
is the required HCF.
In case of Calculation of HCF of more than two numbers, first of all HCF of any
two numbers is calculated and then we find the HCF of this HCF and the third
number and so on. The last HCF will be the required HCF.
Q Find the HCF of 42, 70 and 84.
HCF & LCM