GCF of 735/376, 7154/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 735/376, 7154/978 i.e 49/183864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 735/376, 7154/978.
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 735/376,7154/978?
Given fractions are 735/376,7154/978
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 735/376,7154/978, numerators are 735,7154
Denominators are 376,978
The GCF of 735,7154 is 49 .
LCM of 376,978 is 183864.
The greatest common factor of 735/376,7154/978 = [GCF of 735,7154]/[LCM of 376,978]= 49/183864
Therefore, the GCF of 735/376,7154/978 is 49/183864.
To find the highest common factor of 735,7154, we have to find the factors of both numbers and list the highest common factor.
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The factors of 7154 are 1, 2, 7, 14, 49, 73, 98, 146, 511, 1022, 3577, 7154
The HCF of 735,7154 is 49.
Lets's calculate GCF of 735,7154
| 7 | 735, 7154 |
| 7 | 105, 1022 |
| 15, 146 |
∴ So the GCF of the given numbers is 7 x 7 = 49
Greatest Common Factor of 735,7154 By Matching Biggest Common Factor Method
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Now, list down the factors of 7154
:1,2,7,14,49,73,98,146,511,1022,3577,7154
Greatest Common Factor
We found the factors 735,7154 . The biggest common factor number is the GCF number.
So the greatest common factor 735,7154 is 49.
Lets's calculate LCM of 376,978
| 2 | 376, 978 |
| 188, 489 |
∴ So the LCM of the given numbers is 2 x 188 x 489 = 183864
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 49/183864
Therefore, the GCF of Fractions 735/376,7154/978 is 49/183864
Least Common Multiple of 376,978 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 376,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(376,978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(376,978) x common factors =2 x 1 = 2
LCM(376,978) = ( 376 × 978 ) / 2
LCM(376,978) = 367728 / 2
LCM(376,978) = 183864
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FAQs on GCF of Fractions of 735/376, 7154/978
1. What is the HCF of 735,7154?
The HCF of 735,7154 is 49
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 735/376, 7154/978?
Answer: GCF of Numerators as per given numbers 735/376, 7154/978 is
GCF of Numerators i.e. for 735,7154 is 49
LCM of denominators i.e. for 376,978 is 183864.
Thus, GCF of Fractions is 49/183864.Finally, GCF of Fractions for 735/376, 7154/978 is 49/183864.