GCF of 107/54, 420/562
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 107/54, 420/562 i.e 1/15174 easily. The following is the detailed procedure to determine the greatest common factor of fractions 107/54, 420/562.
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 107/54,420/562?
Given fractions are 107/54,420/562
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 107/54,420/562, numerators are 107,420
Denominators are 54,562
The GCF of 107,420 is 1 .
LCM of 54,562 is 15174.
The greatest common factor of 107/54,420/562 = [GCF of 107,420]/[LCM of 54,562]= 1/15174
Therefore, the GCF of 107/54,420/562 is 1/15174.
To find the highest common factor of 107,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 107 are 1, 107
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 107,420 is 1.
Lets's calculate GCF of 107,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 107,420 By Matching Biggest Common Factor Method
Now, list down the factors of 107
:1,107
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 107,420 . The biggest common factor number is the GCF number.
So the greatest common factor 107,420 is 1.
Lets's calculate LCM of 54,562
| 2 | 54, 562 |
| 27, 281 |
∴ So the LCM of the given numbers is 2 x 27 x 281 = 15174
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15174
Therefore, the GCF of Fractions 107/54,420/562 is 1/15174
Least Common Multiple of 54,562 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 54,562 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,562) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,562) x common factors =2 x 1 = 2
LCM(54,562) = ( 54 × 562 ) / 2
LCM(54,562) = 30348 / 2
LCM(54,562) = 15174
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FAQs on GCF of Fractions of 107/54, 420/562
1. What is the HCF of 107,420?
The HCF of 107,420 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 107/54, 420/562?
Answer: GCF of Numerators as per given numbers 107/54, 420/562 is
GCF of Numerators i.e. for 107,420 is 1
LCM of denominators i.e. for 54,562 is 15174.
Thus, GCF of Fractions is 1/15174.Finally, GCF of Fractions for 107/54, 420/562 is 1/15174.