GCF of 70/14, 84/65, 238/323
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/14, 84/65, 238/323 i.e 14/293930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/14, 84/65, 238/323.
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 70/14,84/65,238/323?
Given fractions are 70/14,84/65,238/323
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 70/14,84/65,238/323, numerators are 70,84,238
Denominators are 14,65,323
The GCF of 70,84,238 is 14 .
LCM of 14,65,323 is 293930.
The greatest common factor of 70/14,84/65,238/323 = [GCF of 70,84,238]/[LCM of 14,65,323]= 14/293930
Therefore, the GCF of 70/14,84/65,238/323 is 14/293930.
To find the highest common factor of 70,84,238, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The HCF of 70,84,238 is 14.
Lets's calculate GCF of 70,84,238
| 2 | 70, 84, 238 |
| 7 | 35, 42, 119 |
| 5, 6, 17 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 70,84,238 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Greatest Common Factor
We found the factors 70,84,238 . The biggest common factor number is the GCF number.
So the greatest common factor 70,84,238 is 14.
Lets's calculate LCM of 14,65,323
Given numbers has no common factors except 1. So, there LCM is their product i.e 293930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/293930
Therefore, the GCF of Fractions 70/14,84/65,238/323 is 14/293930
Least Common Multiple of 14,65,323 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 14,65,323 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,65,323) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(14,65,323) x common factors =1 x 1 = 1
LCM(14,65,323) = ( 14 × 65 × 323 ) / 1
LCM(14,65,323) = 293930 / 1
LCM(14,65,323) = 293930
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FAQs on GCF of Fractions of 70/14, 84/65, 238/323
1. What is the HCF of 70,84,238?
The HCF of 70,84,238 is 14
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 70/14, 84/65, 238/323?
Answer: GCF of Numerators as per given numbers 70/14, 84/65, 238/323 is
GCF of Numerators i.e. for 70,84,238 is 14
LCM of denominators i.e. for 14,65,323 is 293930.
Thus, GCF of Fractions is 14/293930.Finally, GCF of Fractions for 70/14, 84/65, 238/323 is 14/293930.