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Highest Common Factor- HCF : The highest common factor of two or more numbers is the greatest or the largest among the common factors.
Example: G.C.F of 24 and 36
Factors of 24 = 2 x 2 x 2 x 3
Factors of 36 = 2 x 2 x 3 x 3
Common factors = 2 ,2,3
H.C.F = 2 x 2 x 3 = 12
Note : The G.C.F of two co- prime numbers is always 1.
We can use factor tree method or prime factorization method to find the factors of the given numbers.
Some Applications of G.C.F
1) Find the largest number which divides 245 and 1029 leaving the remainder 5 in each case. Solution : As 5 is remainder in each case, so first subtract 5 from each number.
245 -5 =240 and 1029 -5 = 1024
As we have to find the largest number that means we have to find the GCF of 240 and 1024.
Common factors are 2,2,2,2
So GCF = 16
2)Two tankers contain 850 liters and 680 liters of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times. Solution: A container can measure 850 liters of petrol an exact number of times if its capacity in liters is a divisor of 850. Also to measure 680 liters of petrol the capacity in liters must also be divisor of 680.
Therefore , the maximum capacity of the container is the GCF of 850 and 680 in liters.
(use any method to find GCF)
So the GCF of 850 and 680 is 170.
So the capacity of the container = 170 liters.
3)Reduce 289/391 Solution :In order to reduce a given fraction in the lowest terms, we divide its numerator and denominator by their GCF.
So GCF of 289 and 391 is 17
(289 ÷17) /(391÷17) = 17/23 Factors and Multiples