GCF of 766/76, 420/159
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 766/76, 420/159 i.e 2/12084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 766/76, 420/159.
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 766/76,420/159?
Given fractions are 766/76,420/159
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 766/76,420/159, numerators are 766,420
Denominators are 76,159
The GCF of 766,420 is 2 .
LCM of 76,159 is 12084.
The greatest common factor of 766/76,420/159 = [GCF of 766,420]/[LCM of 76,159]= 2/12084
Therefore, the GCF of 766/76,420/159 is 2/12084.
To find the highest common factor of 766,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 766 are 1, 2, 383, 766
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 766,420 is 2.
Lets's calculate GCF of 766,420
| 2 | 766, 420 |
| 383, 210 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 766,420 By Matching Biggest Common Factor Method
Now, list down the factors of 766
:1,2,383,766
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 766,420 . The biggest common factor number is the GCF number.
So the greatest common factor 766,420 is 2.
Lets's calculate LCM of 76,159
Given numbers has no common factors except 1. So, there LCM is their product i.e 12084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12084
Therefore, the GCF of Fractions 766/76,420/159 is 2/12084
Least Common Multiple of 76,159 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 76,159 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,159) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(76,159) x common factors =1 x 1 = 1
LCM(76,159) = ( 76 × 159 ) / 1
LCM(76,159) = 12084 / 1
LCM(76,159) = 12084
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FAQs on GCF of Fractions of 766/76, 420/159
1. What is the HCF of 766,420?
The HCF of 766,420 is 2
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 766/76, 420/159?
Answer: GCF of Numerators as per given numbers 766/76, 420/159 is
GCF of Numerators i.e. for 766,420 is 2
LCM of denominators i.e. for 76,159 is 12084.
Thus, GCF of Fractions is 2/12084.Finally, GCF of Fractions for 766/76, 420/159 is 2/12084.