GCF of 1680/748, 7760/7853
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1680/748, 7760/7853 i.e 80/5874044 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1680/748, 7760/7853.
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 1680/748,7760/7853?
Given fractions are 1680/748,7760/7853
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 1680/748,7760/7853, numerators are 1680,7760
Denominators are 748,7853
The GCF of 1680,7760 is 80 .
LCM of 748,7853 is 5874044.
The greatest common factor of 1680/748,7760/7853 = [GCF of 1680,7760]/[LCM of 748,7853]= 80/5874044
Therefore, the GCF of 1680/748,7760/7853 is 80/5874044.
To find the highest common factor of 1680,7760, we have to find the factors of both numbers and list the highest common factor.
The factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
The factors of 7760 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 97, 194, 388, 485, 776, 970, 1552, 1940, 3880, 7760
The HCF of 1680,7760 is 80.
Lets's calculate GCF of 1680,7760
| 2 | 1680, 7760 |
| 2 | 840, 3880 |
| 2 | 420, 1940 |
| 2 | 210, 970 |
| 5 | 105, 485 |
| 21, 97 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 5 = 80
Greatest Common Factor of 1680,7760 By Matching Biggest Common Factor Method
Now, list down the factors of 1680
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,35,40,42,48,56,60,70,80,84,105,112,120,140,168,210,240,280,336,420,560,840,1680
Now, list down the factors of 7760
:1,2,4,5,8,10,16,20,40,80,97,194,388,485,776,970,1552,1940,3880,7760
Greatest Common Factor
We found the factors 1680,7760 . The biggest common factor number is the GCF number.
So the greatest common factor 1680,7760 is 80.
Lets's calculate LCM of 748,7853
Given numbers has no common factors except 1. So, there LCM is their product i.e 5874044
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 80/5874044
Therefore, the GCF of Fractions 1680/748,7760/7853 is 80/5874044
Least Common Multiple of 748,7853 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 748,7853 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(748,7853) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(748,7853) x common factors =1 x 1 = 1
LCM(748,7853) = ( 748 × 7853 ) / 1
LCM(748,7853) = 5874044 / 1
LCM(748,7853) = 5874044
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FAQs on GCF of Fractions of 1680/748, 7760/7853
1. What is the HCF of 1680,7760?
The HCF of 1680,7760 is 80
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 1680/748, 7760/7853?
Answer: GCF of Numerators as per given numbers 1680/748, 7760/7853 is
GCF of Numerators i.e. for 1680,7760 is 80
LCM of denominators i.e. for 748,7853 is 5874044.
Thus, GCF of Fractions is 80/5874044.Finally, GCF of Fractions for 1680/748, 7760/7853 is 80/5874044.