GCF of 1696/344, 3786/856
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1696/344, 3786/856 i.e 2/36808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1696/344, 3786/856.
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 1696/344,3786/856?
Given fractions are 1696/344,3786/856
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 1696/344,3786/856, numerators are 1696,3786
Denominators are 344,856
The GCF of 1696,3786 is 2 .
LCM of 344,856 is 36808.
The greatest common factor of 1696/344,3786/856 = [GCF of 1696,3786]/[LCM of 344,856]= 2/36808
Therefore, the GCF of 1696/344,3786/856 is 2/36808.
To find the highest common factor of 1696,3786, we have to find the factors of both numbers and list the highest common factor.
The factors of 1696 are 1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848, 1696
The factors of 3786 are 1, 2, 3, 6, 631, 1262, 1893, 3786
The HCF of 1696,3786 is 2.
Lets's calculate GCF of 1696,3786
| 2 | 1696, 3786 |
| 848, 1893 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1696,3786 By Matching Biggest Common Factor Method
Now, list down the factors of 1696
:1,2,4,8,16,32,53,106,212,424,848,1696
Now, list down the factors of 3786
:1,2,3,6,631,1262,1893,3786
Greatest Common Factor
We found the factors 1696,3786 . The biggest common factor number is the GCF number.
So the greatest common factor 1696,3786 is 2.
Lets's calculate LCM of 344,856
| 2 | 344, 856 |
| 2 | 172, 428 |
| 2 | 86, 214 |
| 43, 107 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 43 x 107 = 36808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/36808
Therefore, the GCF of Fractions 1696/344,3786/856 is 2/36808
Least Common Multiple of 344,856 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 344,856 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(344,856) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(344,856) x common factors =8 x 1 = 8
LCM(344,856) = ( 344 × 856 ) / 8
LCM(344,856) = 294464 / 8
LCM(344,856) = 36808
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FAQs on GCF of Fractions of 1696/344, 3786/856
1. What is the HCF of 1696,3786?
The HCF of 1696,3786 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 1696/344, 3786/856?
Answer: GCF of Numerators as per given numbers 1696/344, 3786/856 is
GCF of Numerators i.e. for 1696,3786 is 2
LCM of denominators i.e. for 344,856 is 36808.
Thus, GCF of Fractions is 2/36808.Finally, GCF of Fractions for 1696/344, 3786/856 is 2/36808.