GCF of 505/75, 420/776
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 505/75, 420/776 i.e 5/58200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 505/75, 420/776.
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 505/75,420/776?
Given fractions are 505/75,420/776
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 505/75,420/776, numerators are 505,420
Denominators are 75,776
The GCF of 505,420 is 5 .
LCM of 75,776 is 58200.
The greatest common factor of 505/75,420/776 = [GCF of 505,420]/[LCM of 75,776]= 5/58200
Therefore, the GCF of 505/75,420/776 is 5/58200.
To find the highest common factor of 505,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 505 are 1, 5, 101, 505
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 505,420 is 5.
Lets's calculate GCF of 505,420
| 5 | 505, 420 |
| 101, 84 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 505,420 By Matching Biggest Common Factor Method
Now, list down the factors of 505
:1,5,101,505
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 505,420 . The biggest common factor number is the GCF number.
So the greatest common factor 505,420 is 5.
Lets's calculate LCM of 75,776
Given numbers has no common factors except 1. So, there LCM is their product i.e 58200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/58200
Therefore, the GCF of Fractions 505/75,420/776 is 5/58200
Least Common Multiple of 75,776 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 75,776 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,776) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,776) x common factors =1 x 1 = 1
LCM(75,776) = ( 75 × 776 ) / 1
LCM(75,776) = 58200 / 1
LCM(75,776) = 58200
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FAQs on GCF of Fractions of 505/75, 420/776
1. What is the HCF of 505,420?
The HCF of 505,420 is 5
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 505/75, 420/776?
Answer: GCF of Numerators as per given numbers 505/75, 420/776 is
GCF of Numerators i.e. for 505,420 is 5
LCM of denominators i.e. for 75,776 is 58200.
Thus, GCF of Fractions is 5/58200.Finally, GCF of Fractions for 505/75, 420/776 is 5/58200.