GCF of 781/706, 840/614
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 781/706, 840/614 i.e 1/216742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 781/706, 840/614.
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 781/706,840/614?
Given fractions are 781/706,840/614
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 781/706,840/614, numerators are 781,840
Denominators are 706,614
The GCF of 781,840 is 1 .
LCM of 706,614 is 216742.
The greatest common factor of 781/706,840/614 = [GCF of 781,840]/[LCM of 706,614]= 1/216742
Therefore, the GCF of 781/706,840/614 is 1/216742.
To find the highest common factor of 781,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 781 are 1, 11, 71, 781
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 781,840 is 1.
Lets's calculate GCF of 781,840
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 781,840 By Matching Biggest Common Factor Method
Now, list down the factors of 781
:1,11,71,781
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 781,840 . The biggest common factor number is the GCF number.
So the greatest common factor 781,840 is 1.
Lets's calculate LCM of 706,614
| 2 | 706, 614 |
| 353, 307 |
∴ So the LCM of the given numbers is 2 x 353 x 307 = 216742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/216742
Therefore, the GCF of Fractions 781/706,840/614 is 1/216742
Least Common Multiple of 706,614 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 706,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,614) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(706,614) x common factors =2 x 1 = 2
LCM(706,614) = ( 706 × 614 ) / 2
LCM(706,614) = 433484 / 2
LCM(706,614) = 216742
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FAQs on GCF of Fractions of 781/706, 840/614
1. What is the HCF of 781,840?
The HCF of 781,840 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 781/706, 840/614?
Answer: GCF of Numerators as per given numbers 781/706, 840/614 is
GCF of Numerators i.e. for 781,840 is 1
LCM of denominators i.e. for 706,614 is 216742.
Thus, GCF of Fractions is 1/216742.Finally, GCF of Fractions for 781/706, 840/614 is 1/216742.