GCF of 89/278, 975/678, 580/339
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 89/278, 975/678, 580/339 i.e 1/94242 easily. The following is the detailed procedure to determine the greatest common factor of fractions 89/278, 975/678, 580/339.
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 89/278,975/678,580/339?
Given fractions are 89/278,975/678,580/339
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 89/278,975/678,580/339, numerators are 89,975,580
Denominators are 278,678,339
The GCF of 89,975,580 is 1 .
LCM of 278,678,339 is 94242.
The greatest common factor of 89/278,975/678,580/339 = [GCF of 89,975,580]/[LCM of 278,678,339]= 1/94242
Therefore, the GCF of 89/278,975/678,580/339 is 1/94242.
To find the highest common factor of 89,975,580, we have to find the factors of both numbers and list the highest common factor.
The factors of 89 are 1, 89
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The HCF of 89,975,580 is 1.
Lets's calculate GCF of 89,975,580
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 89,975,580 By Matching Biggest Common Factor Method
Now, list down the factors of 89
:1,89
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Greatest Common Factor
We found the factors 89,975,580 . The biggest common factor number is the GCF number.
So the greatest common factor 89,975,580 is 1.
Lets's calculate LCM of 278,678,339
| 2 | 278, 678, 339 |
| 3 | 139, 339, 339 |
| 113 | 139, 113, 113 |
| 139, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 113 x 139 x 1 x 1 = 94242
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/94242
Therefore, the GCF of Fractions 89/278,975/678,580/339 is 1/94242
Least Common Multiple of 278,678,339 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 278,678,339 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(278,678,339) = 1
common factors(in case of two or more numbers have common factors) = 678
GCF(278,678,339) x common factors =1 x 678 = 678
LCM(278,678,339) = ( 278 × 678 × 339 ) / 678
LCM(278,678,339) = 63896076 / 678
LCM(278,678,339) = 94242
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FAQs on GCF of Fractions of 89/278, 975/678, 580/339
1. What is the HCF of 89,975,580?
The HCF of 89,975,580 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 89/278, 975/678, 580/339?
Answer: GCF of Numerators as per given numbers 89/278, 975/678, 580/339 is
GCF of Numerators i.e. for 89,975,580 is 1
LCM of denominators i.e. for 278,678,339 is 94242.
Thus, GCF of Fractions is 1/94242.Finally, GCF of Fractions for 89/278, 975/678, 580/339 is 1/94242.