GCF of 217/54, 527/557
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 217/54, 527/557 i.e 31/30078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/54, 527/557.
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 217/54,527/557?
Given fractions are 217/54,527/557
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 217/54,527/557, numerators are 217,527
Denominators are 54,557
The GCF of 217,527 is 31 .
LCM of 54,557 is 30078.
The greatest common factor of 217/54,527/557 = [GCF of 217,527]/[LCM of 54,557]= 31/30078
Therefore, the GCF of 217/54,527/557 is 31/30078.
To find the highest common factor of 217,527, we have to find the factors of both numbers and list the highest common factor.
The factors of 217 are 1, 7, 31, 217
The factors of 527 are 1, 17, 31, 527
The HCF of 217,527 is 31.
Lets's calculate GCF of 217,527
| 31 | 217, 527 |
| 7, 17 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 217,527 By Matching Biggest Common Factor Method
Now, list down the factors of 217
:1,7,31,217
Now, list down the factors of 527
:1,17,31,527
Greatest Common Factor
We found the factors 217,527 . The biggest common factor number is the GCF number.
So the greatest common factor 217,527 is 31.
Lets's calculate LCM of 54,557
Given numbers has no common factors except 1. So, there LCM is their product i.e 30078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/30078
Therefore, the GCF of Fractions 217/54,527/557 is 31/30078
Least Common Multiple of 54,557 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 54,557 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,557) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(54,557) x common factors =1 x 1 = 1
LCM(54,557) = ( 54 × 557 ) / 1
LCM(54,557) = 30078 / 1
LCM(54,557) = 30078
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FAQs on GCF of Fractions of 217/54, 527/557
1. What is the HCF of 217,527?
The HCF of 217,527 is 31
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 217/54, 527/557?
Answer: GCF of Numerators as per given numbers 217/54, 527/557 is
GCF of Numerators i.e. for 217,527 is 31
LCM of denominators i.e. for 54,557 is 30078.
Thus, GCF of Fractions is 31/30078.Finally, GCF of Fractions for 217/54, 527/557 is 31/30078.