GCF of 213/34, 114/735
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 213/34, 114/735 i.e 3/24990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/34, 114/735.
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 213/34,114/735?
Given fractions are 213/34,114/735
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 213/34,114/735, numerators are 213,114
Denominators are 34,735
The GCF of 213,114 is 3 .
LCM of 34,735 is 24990.
The greatest common factor of 213/34,114/735 = [GCF of 213,114]/[LCM of 34,735]= 3/24990
Therefore, the GCF of 213/34,114/735 is 3/24990.
To find the highest common factor of 213,114, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The HCF of 213,114 is 3.
Lets's calculate GCF of 213,114
| 3 | 213, 114 |
| 71, 38 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 213,114 By Matching Biggest Common Factor Method
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors 213,114 . The biggest common factor number is the GCF number.
So the greatest common factor 213,114 is 3.
Lets's calculate LCM of 34,735
Given numbers has no common factors except 1. So, there LCM is their product i.e 24990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/24990
Therefore, the GCF of Fractions 213/34,114/735 is 3/24990
Least Common Multiple of 34,735 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 34,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,735) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(34,735) x common factors =1 x 1 = 1
LCM(34,735) = ( 34 × 735 ) / 1
LCM(34,735) = 24990 / 1
LCM(34,735) = 24990
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FAQs on GCF of Fractions of 213/34, 114/735
1. What is the HCF of 213,114?
The HCF of 213,114 is 3
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 213/34, 114/735?
Answer: GCF of Numerators as per given numbers 213/34, 114/735 is
GCF of Numerators i.e. for 213,114 is 3
LCM of denominators i.e. for 34,735 is 24990.
Thus, GCF of Fractions is 3/24990.Finally, GCF of Fractions for 213/34, 114/735 is 3/24990.