GCF of 385/864, 1540/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 385/864, 1540/714 i.e 385/102816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 385/864, 1540/714.
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 385/864,1540/714?
Given fractions are 385/864,1540/714
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 385/864,1540/714, numerators are 385,1540
Denominators are 864,714
The GCF of 385,1540 is 385 .
LCM of 864,714 is 102816.
The greatest common factor of 385/864,1540/714 = [GCF of 385,1540]/[LCM of 864,714]= 385/102816
Therefore, the GCF of 385/864,1540/714 is 385/102816.
To find the highest common factor of 385,1540, we have to find the factors of both numbers and list the highest common factor.
The factors of 385 are 1, 5, 7, 11, 35, 55, 77, 385
The factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540
The HCF of 385,1540 is 385.
Lets's calculate GCF of 385,1540
| 5 | 385, 1540 |
| 7 | 77, 308 |
| 11 | 11, 44 |
| 1, 4 |
∴ So the GCF of the given numbers is 5 x 7 x 11 = 385
Greatest Common Factor of 385,1540 By Matching Biggest Common Factor Method
Now, list down the factors of 385
:1,5,7,11,35,55,77,385
Now, list down the factors of 1540
:1,2,4,5,7,10,11,14,20,22,28,35,44,55,70,77,110,140,154,220,308,385,770,1540
Greatest Common Factor
We found the factors 385,1540 . The biggest common factor number is the GCF number.
So the greatest common factor 385,1540 is 385.
Lets's calculate LCM of 864,714
| 2 | 864, 714 |
| 3 | 432, 357 |
| 144, 119 |
∴ So the LCM of the given numbers is 2 x 3 x 144 x 119 = 102816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 385/102816
Therefore, the GCF of Fractions 385/864,1540/714 is 385/102816
Least Common Multiple of 864,714 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 864,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(864,714) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(864,714) x common factors =6 x 1 = 6
LCM(864,714) = ( 864 × 714 ) / 6
LCM(864,714) = 616896 / 6
LCM(864,714) = 102816
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FAQs on GCF of Fractions of 385/864, 1540/714
1. What is the HCF of 385,1540?
The HCF of 385,1540 is 385
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 385/864, 1540/714?
Answer: GCF of Numerators as per given numbers 385/864, 1540/714 is
GCF of Numerators i.e. for 385,1540 is 385
LCM of denominators i.e. for 864,714 is 102816.
Thus, GCF of Fractions is 385/102816.Finally, GCF of Fractions for 385/864, 1540/714 is 385/102816.