GCF of 370/17, 278/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 370/17, 278/414 i.e 2/7038 easily. The following is the detailed procedure to determine the greatest common factor of fractions 370/17, 278/414.
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 370/17,278/414?
Given fractions are 370/17,278/414
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 370/17,278/414, numerators are 370,278
Denominators are 17,414
The GCF of 370,278 is 2 .
LCM of 17,414 is 7038.
The greatest common factor of 370/17,278/414 = [GCF of 370,278]/[LCM of 17,414]= 2/7038
Therefore, the GCF of 370/17,278/414 is 2/7038.
To find the highest common factor of 370,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370
The factors of 278 are 1, 2, 139, 278
The HCF of 370,278 is 2.
Lets's calculate GCF of 370,278
| 2 | 370, 278 |
| 185, 139 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 370,278 By Matching Biggest Common Factor Method
Now, list down the factors of 370
:1,2,5,10,37,74,185,370
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 370,278 . The biggest common factor number is the GCF number.
So the greatest common factor 370,278 is 2.
Lets's calculate LCM of 17,414
Given numbers has no common factors except 1. So, there LCM is their product i.e 7038
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7038
Therefore, the GCF of Fractions 370/17,278/414 is 2/7038
Least Common Multiple of 17,414 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 17,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,414) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(17,414) x common factors =1 x 1 = 1
LCM(17,414) = ( 17 × 414 ) / 1
LCM(17,414) = 7038 / 1
LCM(17,414) = 7038
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FAQs on GCF of Fractions of 370/17, 278/414
1. What is the HCF of 370,278?
The HCF of 370,278 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 370/17, 278/414?
Answer: GCF of Numerators as per given numbers 370/17, 278/414 is
GCF of Numerators i.e. for 370,278 is 2
LCM of denominators i.e. for 17,414 is 7038.
Thus, GCF of Fractions is 2/7038.Finally, GCF of Fractions for 370/17, 278/414 is 2/7038.