GCF of 45/64, 259/49, 408/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 45/64, 259/49, 408/219 i.e 1/686784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 45/64, 259/49, 408/219.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 45/64,259/49,408/219?
Given fractions are 45/64,259/49,408/219
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 45/64,259/49,408/219, numerators are 45,259,408
Denominators are 64,49,219
The GCF of 45,259,408 is 1 .
LCM of 64,49,219 is 686784.
The greatest common factor of 45/64,259/49,408/219 = [GCF of 45,259,408]/[LCM of 64,49,219]= 1/686784
Therefore, the GCF of 45/64,259/49,408/219 is 1/686784.
To find the highest common factor of 45,259,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 259 are 1, 7, 37, 259
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 45,259,408 is 1.
Lets's calculate GCF of 45,259,408
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 45,259,408 By Matching Biggest Common Factor Method
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 259
:1,7,37,259
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 45,259,408 . The biggest common factor number is the GCF number.
So the greatest common factor 45,259,408 is 1.
Lets's calculate LCM of 64,49,219
Given numbers has no common factors except 1. So, there LCM is their product i.e 686784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/686784
Therefore, the GCF of Fractions 45/64,259/49,408/219 is 1/686784
Least Common Multiple of 64,49,219 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 64,49,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,49,219) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(64,49,219) x common factors =1 x 1 = 1
LCM(64,49,219) = ( 64 × 49 × 219 ) / 1
LCM(64,49,219) = 686784 / 1
LCM(64,49,219) = 686784
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FAQs on GCF of Fractions of 45/64, 259/49, 408/219
1. What is the HCF of 45,259,408?
The HCF of 45,259,408 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 45/64, 259/49, 408/219?
Answer: GCF of Numerators as per given numbers 45/64, 259/49, 408/219 is
GCF of Numerators i.e. for 45,259,408 is 1
LCM of denominators i.e. for 64,49,219 is 686784.
Thus, GCF of Fractions is 1/686784.Finally, GCF of Fractions for 45/64, 259/49, 408/219 is 1/686784.