GCF of 308/254, 840/758
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 308/254, 840/758 i.e 28/96266 easily. The following is the detailed procedure to determine the greatest common factor of fractions 308/254, 840/758.
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 308/254,840/758?
Given fractions are 308/254,840/758
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 308/254,840/758, numerators are 308,840
Denominators are 254,758
The GCF of 308,840 is 28 .
LCM of 254,758 is 96266.
The greatest common factor of 308/254,840/758 = [GCF of 308,840]/[LCM of 254,758]= 28/96266
Therefore, the GCF of 308/254,840/758 is 28/96266.
To find the highest common factor of 308,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
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 308,840 is 28.
Lets's calculate GCF of 308,840
| 2 | 308, 840 |
| 2 | 154, 420 |
| 7 | 77, 210 |
| 11, 30 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 308,840 By Matching Biggest Common Factor Method
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
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 308,840 . The biggest common factor number is the GCF number.
So the greatest common factor 308,840 is 28.
Lets's calculate LCM of 254,758
| 2 | 254, 758 |
| 127, 379 |
∴ So the LCM of the given numbers is 2 x 127 x 379 = 96266
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/96266
Therefore, the GCF of Fractions 308/254,840/758 is 28/96266
Least Common Multiple of 254,758 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 254,758 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(254,758) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(254,758) x common factors =2 x 1 = 2
LCM(254,758) = ( 254 × 758 ) / 2
LCM(254,758) = 192532 / 2
LCM(254,758) = 96266
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FAQs on GCF of Fractions of 308/254, 840/758
1. What is the HCF of 308,840?
The HCF of 308,840 is 28
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 308/254, 840/758?
Answer: GCF of Numerators as per given numbers 308/254, 840/758 is
GCF of Numerators i.e. for 308,840 is 28
LCM of denominators i.e. for 254,758 is 96266.
Thus, GCF of Fractions is 28/96266.Finally, GCF of Fractions for 308/254, 840/758 is 28/96266.