GCF of 140/735, 214/538
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 140/735, 214/538 i.e 2/395430 easily. The following is the detailed procedure to determine the greatest common factor of fractions 140/735, 214/538.
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 140/735,214/538?
Given fractions are 140/735,214/538
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 140/735,214/538, numerators are 140,214
Denominators are 735,538
The GCF of 140,214 is 2 .
LCM of 735,538 is 395430.
The greatest common factor of 140/735,214/538 = [GCF of 140,214]/[LCM of 735,538]= 2/395430
Therefore, the GCF of 140/735,214/538 is 2/395430.
To find the highest common factor of 140,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The factors of 214 are 1, 2, 107, 214
The HCF of 140,214 is 2.
Lets's calculate GCF of 140,214
| 2 | 140, 214 |
| 70, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 140,214 By Matching Biggest Common Factor Method
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 140,214 . The biggest common factor number is the GCF number.
So the greatest common factor 140,214 is 2.
Lets's calculate LCM of 735,538
Given numbers has no common factors except 1. So, there LCM is their product i.e 395430
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/395430
Therefore, the GCF of Fractions 140/735,214/538 is 2/395430
Least Common Multiple of 735,538 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 735,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(735,538) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(735,538) x common factors =1 x 1 = 1
LCM(735,538) = ( 735 × 538 ) / 1
LCM(735,538) = 395430 / 1
LCM(735,538) = 395430
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FAQs on GCF of Fractions of 140/735, 214/538
1. What is the HCF of 140,214?
The HCF of 140,214 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 140/735, 214/538?
Answer: GCF of Numerators as per given numbers 140/735, 214/538 is
GCF of Numerators i.e. for 140,214 is 2
LCM of denominators i.e. for 735,538 is 395430.
Thus, GCF of Fractions is 2/395430.Finally, GCF of Fractions for 140/735, 214/538 is 2/395430.