GCF of 504/781, 378/829
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 504/781, 378/829 i.e 126/647449 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/781, 378/829.
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 504/781,378/829?
Given fractions are 504/781,378/829
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 504/781,378/829, numerators are 504,378
Denominators are 781,829
The GCF of 504,378 is 126 .
LCM of 781,829 is 647449.
The greatest common factor of 504/781,378/829 = [GCF of 504,378]/[LCM of 781,829]= 126/647449
Therefore, the GCF of 504/781,378/829 is 126/647449.
To find the highest common factor of 504,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 504,378 is 126.
Lets's calculate GCF of 504,378
| 2 | 504, 378 |
| 3 | 252, 189 |
| 3 | 84, 63 |
| 7 | 28, 21 |
| 4, 3 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 7 = 126
Greatest Common Factor of 504,378 By Matching Biggest Common Factor Method
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 504,378 . The biggest common factor number is the GCF number.
So the greatest common factor 504,378 is 126.
Lets's calculate LCM of 781,829
Given numbers has no common factors except 1. So, there LCM is their product i.e 647449
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 126/647449
Therefore, the GCF of Fractions 504/781,378/829 is 126/647449
Least Common Multiple of 781,829 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 781,829 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(781,829) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(781,829) x common factors =1 x 1 = 1
LCM(781,829) = ( 781 × 829 ) / 1
LCM(781,829) = 647449 / 1
LCM(781,829) = 647449
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FAQs on GCF of Fractions of 504/781, 378/829
1. What is the HCF of 504,378?
The HCF of 504,378 is 126
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 504/781, 378/829?
Answer: GCF of Numerators as per given numbers 504/781, 378/829 is
GCF of Numerators i.e. for 504,378 is 126
LCM of denominators i.e. for 781,829 is 647449.
Thus, GCF of Fractions is 126/647449.Finally, GCF of Fractions for 504/781, 378/829 is 126/647449.