GCF of 67/214, 34/731, 782/392
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 67/214, 34/731, 782/392 i.e 1/30661064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/214, 34/731, 782/392.
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 67/214,34/731,782/392?
Given fractions are 67/214,34/731,782/392
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 67/214,34/731,782/392, numerators are 67,34,782
Denominators are 214,731,392
The GCF of 67,34,782 is 1 .
LCM of 214,731,392 is 30661064.
The greatest common factor of 67/214,34/731,782/392 = [GCF of 67,34,782]/[LCM of 214,731,392]= 1/30661064
Therefore, the GCF of 67/214,34/731,782/392 is 1/30661064.
To find the highest common factor of 67,34,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 67 are 1, 67
The factors of 34 are 1, 2, 17, 34
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 67,34,782 is 1.
Lets's calculate GCF of 67,34,782
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 67,34,782 By Matching Biggest Common Factor Method
Now, list down the factors of 67
:1,67
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 67,34,782 . The biggest common factor number is the GCF number.
So the greatest common factor 67,34,782 is 1.
Lets's calculate LCM of 214,731,392
| 2 | 214, 731, 392 |
| 107, 731, 196 |
∴ So the LCM of the given numbers is 2 x 107 x 731 x 196 = 30661064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30661064
Therefore, the GCF of Fractions 67/214,34/731,782/392 is 1/30661064
Least Common Multiple of 214,731,392 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 214,731,392 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,731,392) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(214,731,392) x common factors =1 x 2 = 2
LCM(214,731,392) = ( 214 × 731 × 392 ) / 2
LCM(214,731,392) = 61322128 / 2
LCM(214,731,392) = 30661064
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FAQs on GCF of Fractions of 67/214, 34/731, 782/392
1. What is the HCF of 67,34,782?
The HCF of 67,34,782 is 1
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 67/214, 34/731, 782/392?
Answer: GCF of Numerators as per given numbers 67/214, 34/731, 782/392 is
GCF of Numerators i.e. for 67,34,782 is 1
LCM of denominators i.e. for 214,731,392 is 30661064.
Thus, GCF of Fractions is 1/30661064.Finally, GCF of Fractions for 67/214, 34/731, 782/392 is 1/30661064.