Factors and Multiples
If number x divides another number y then x is a factor of number y.
In this case, y is a multiple of x.
Highest Common Factor (HCF)
The HCF of two or more than two numbers is the greatest number that divided each of them exactly.
Methods of finding the HCF of two numbers
a) Factorization Method - Each one of the given numbers are expressed as the product of prime factors. The product of least powers of common prime factors gives the HCF of the numbers.
If number x divides another number y then x is a factor of number y.
In this case, y is a multiple of x.
Highest Common Factor (HCF)
The HCF of two or more than two numbers is the greatest number that divided each of them exactly.
Methods of finding the HCF of two numbers
a) Factorization Method - Each one of the given numbers are expressed as the product of prime factors. The product of least powers of common prime factors gives the HCF of the numbers.
b) Division Method - Suppose we have to find the HCF of two given numbers. We divide the larger number by the smaller one. Then the divisor is divided by the remainder. This process of dividing the preceding divisor by the remainder is repeated until zero is obtained as the remainder. The last divisor is the required HCF
Method of finding the HCF of more than two numbers
Suppose we have to find the H.C.F. of three numbers, then, HCF of three numbers is the [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given numbers.
Least Common Multiple (LCM)
The least number that is exactly divisible by each one of the given numbers is called the LCM.
Methods for finding the LCM of a given set of numbers
a) Factorization Method - Each one of the given numbers is resolved into product of prime factors. The product of the highest powers of all factors is the required LCM.
b) Division Method - The given numbers are arranged in a row in any order. These numbers are divided by a number which divides at least two numbers exactly. The numbers which are not divisible are carried forward. This process is repeated until all the numbers are divided. The product of the divisors is the required LCM.
Product of two numbers = Product of their HCF and LCM
HCF and LCM of Fractions
a) HCF = HCF of numerator/LCM of denominator
b) LCM = LCM of numerator/HCF of denominator
HCF and LCM of Decimal Fractions
In the given set of numbers, zeros are annexed to some numbers so that the number of decimal places becomes the same. Considering these numbers without decimal point, the HCF or LCM is found out. Now in the result as many decimal places are marked off as there were in the given numbers.
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