GCF of 106/560, 768/308
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 106/560, 768/308 i.e 2/6160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 106/560, 768/308.
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 106/560,768/308?
Given fractions are 106/560,768/308
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 106/560,768/308, numerators are 106,768
Denominators are 560,308
The GCF of 106,768 is 2 .
LCM of 560,308 is 6160.
The greatest common factor of 106/560,768/308 = [GCF of 106,768]/[LCM of 560,308]= 2/6160
Therefore, the GCF of 106/560,768/308 is 2/6160.
To find the highest common factor of 106,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 106 are 1, 2, 53, 106
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 106,768 is 2.
Lets's calculate GCF of 106,768
| 2 | 106, 768 |
| 53, 384 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 106,768 By Matching Biggest Common Factor Method
Now, list down the factors of 106
:1,2,53,106
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 106,768 . The biggest common factor number is the GCF number.
So the greatest common factor 106,768 is 2.
Lets's calculate LCM of 560,308
| 2 | 560, 308 |
| 2 | 280, 154 |
| 7 | 140, 77 |
| 20, 11 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 20 x 11 = 6160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6160
Therefore, the GCF of Fractions 106/560,768/308 is 2/6160
Least Common Multiple of 560,308 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 560,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(560,308) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(560,308) x common factors =28 x 1 = 28
LCM(560,308) = ( 560 × 308 ) / 28
LCM(560,308) = 172480 / 28
LCM(560,308) = 6160
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FAQs on GCF of Fractions of 106/560, 768/308
1. What is the HCF of 106,768?
The HCF of 106,768 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 106/560, 768/308?
Answer: GCF of Numerators as per given numbers 106/560, 768/308 is
GCF of Numerators i.e. for 106,768 is 2
LCM of denominators i.e. for 560,308 is 6160.
Thus, GCF of Fractions is 2/6160.Finally, GCF of Fractions for 106/560, 768/308 is 2/6160.