GCF of 527/382, 577/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 527/382, 577/414 i.e 1/79074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 527/382, 577/414.
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 527/382,577/414?
Given fractions are 527/382,577/414
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 527/382,577/414, numerators are 527,577
Denominators are 382,414
The GCF of 527,577 is 1 .
LCM of 382,414 is 79074.
The greatest common factor of 527/382,577/414 = [GCF of 527,577]/[LCM of 382,414]= 1/79074
Therefore, the GCF of 527/382,577/414 is 1/79074.
To find the highest common factor of 527,577, we have to find the factors of both numbers and list the highest common factor.
The factors of 527 are 1, 17, 31, 527
The factors of 577 are 1, 577
The HCF of 527,577 is 1.
Lets's calculate GCF of 527,577
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 527,577 By Matching Biggest Common Factor Method
Now, list down the factors of 527
:1,17,31,527
Now, list down the factors of 577
:1,577
Greatest Common Factor
We found the factors 527,577 . The biggest common factor number is the GCF number.
So the greatest common factor 527,577 is 1.
Lets's calculate LCM of 382,414
| 2 | 382, 414 |
| 191, 207 |
∴ So the LCM of the given numbers is 2 x 191 x 207 = 79074
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/79074
Therefore, the GCF of Fractions 527/382,577/414 is 1/79074
Least Common Multiple of 382,414 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 382,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,414) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(382,414) x common factors =2 x 1 = 2
LCM(382,414) = ( 382 × 414 ) / 2
LCM(382,414) = 158148 / 2
LCM(382,414) = 79074
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FAQs on GCF of Fractions of 527/382, 577/414
1. What is the HCF of 527,577?
The HCF of 527,577 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 527/382, 577/414?
Answer: GCF of Numerators as per given numbers 527/382, 577/414 is
GCF of Numerators i.e. for 527,577 is 1
LCM of denominators i.e. for 382,414 is 79074.
Thus, GCF of Fractions is 1/79074.Finally, GCF of Fractions for 527/382, 577/414 is 1/79074.