GCF of 420/20, 117/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 420/20, 117/578 i.e 3/5780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/20, 117/578.
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 420/20,117/578?
Given fractions are 420/20,117/578
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 420/20,117/578, numerators are 420,117
Denominators are 20,578
The GCF of 420,117 is 3 .
LCM of 20,578 is 5780.
The greatest common factor of 420/20,117/578 = [GCF of 420,117]/[LCM of 20,578]= 3/5780
Therefore, the GCF of 420/20,117/578 is 3/5780.
To find the highest common factor of 420,117, we have to find the factors of both numbers and list the highest common factor.
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 factors of 117 are 1, 3, 9, 13, 39, 117
The HCF of 420,117 is 3.
Lets's calculate GCF of 420,117
| 3 | 420, 117 |
| 140, 39 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 420,117 By Matching Biggest Common Factor Method
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
Now, list down the factors of 117
:1,3,9,13,39,117
Greatest Common Factor
We found the factors 420,117 . The biggest common factor number is the GCF number.
So the greatest common factor 420,117 is 3.
Lets's calculate LCM of 20,578
| 2 | 20, 578 |
| 10, 289 |
∴ So the LCM of the given numbers is 2 x 10 x 289 = 5780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/5780
Therefore, the GCF of Fractions 420/20,117/578 is 3/5780
Least Common Multiple of 20,578 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 20,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,578) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(20,578) x common factors =2 x 1 = 2
LCM(20,578) = ( 20 × 578 ) / 2
LCM(20,578) = 11560 / 2
LCM(20,578) = 5780
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FAQs on GCF of Fractions of 420/20, 117/578
1. What is the HCF of 420,117?
The HCF of 420,117 is 3
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 420/20, 117/578?
Answer: GCF of Numerators as per given numbers 420/20, 117/578 is
GCF of Numerators i.e. for 420,117 is 3
LCM of denominators i.e. for 20,578 is 5780.
Thus, GCF of Fractions is 3/5780.Finally, GCF of Fractions for 420/20, 117/578 is 3/5780.