GCF of 49/76, 638/84, 428/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 49/76, 638/84, 428/414 i.e 1/110124 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/76, 638/84, 428/414.
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 49/76,638/84,428/414?
Given fractions are 49/76,638/84,428/414
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 49/76,638/84,428/414, numerators are 49,638,428
Denominators are 76,84,414
The GCF of 49,638,428 is 1 .
LCM of 76,84,414 is 110124.
The greatest common factor of 49/76,638/84,428/414 = [GCF of 49,638,428]/[LCM of 76,84,414]= 1/110124
Therefore, the GCF of 49/76,638/84,428/414 is 1/110124.
To find the highest common factor of 49,638,428, we have to find the factors of both numbers and list the highest common factor.
The factors of 49 are 1, 7, 49
The factors of 638 are 1, 2, 11, 22, 29, 58, 319, 638
The factors of 428 are 1, 2, 4, 107, 214, 428
The HCF of 49,638,428 is 1.
Lets's calculate GCF of 49,638,428
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 49,638,428 By Matching Biggest Common Factor Method
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 638
:1,2,11,22,29,58,319,638
Now, list down the factors of 428
:1,2,4,107,214,428
Greatest Common Factor
We found the factors 49,638,428 . The biggest common factor number is the GCF number.
So the greatest common factor 49,638,428 is 1.
Lets's calculate LCM of 76,84,414
| 2 | 76, 84, 414 |
| 2 | 38, 42, 207 |
| 3 | 19, 21, 207 |
| 19, 7, 69 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 7 x 69 = 110124
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/110124
Therefore, the GCF of Fractions 49/76,638/84,428/414 is 1/110124
Least Common Multiple of 76,84,414 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 76,84,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,84,414) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(76,84,414) x common factors =2 x 12 = 24
LCM(76,84,414) = ( 76 × 84 × 414 ) / 24
LCM(76,84,414) = 2642976 / 24
LCM(76,84,414) = 110124
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 49/76, 638/84, 428/414
1. What is the HCF of 49,638,428?
The HCF of 49,638,428 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 49/76, 638/84, 428/414?
Answer: GCF of Numerators as per given numbers 49/76, 638/84, 428/414 is
GCF of Numerators i.e. for 49,638,428 is 1
LCM of denominators i.e. for 76,84,414 is 110124.
Thus, GCF of Fractions is 1/110124.Finally, GCF of Fractions for 49/76, 638/84, 428/414 is 1/110124.