GCF of 772/21, 678/758
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 772/21, 678/758 i.e 2/15918 easily. The following is the detailed procedure to determine the greatest common factor of fractions 772/21, 678/758.
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 772/21,678/758?
Given fractions are 772/21,678/758
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 772/21,678/758, numerators are 772,678
Denominators are 21,758
The GCF of 772,678 is 2 .
LCM of 21,758 is 15918.
The greatest common factor of 772/21,678/758 = [GCF of 772,678]/[LCM of 21,758]= 2/15918
Therefore, the GCF of 772/21,678/758 is 2/15918.
To find the highest common factor of 772,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 772 are 1, 2, 4, 193, 386, 772
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 772,678 is 2.
Lets's calculate GCF of 772,678
| 2 | 772, 678 |
| 386, 339 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 772,678 By Matching Biggest Common Factor Method
Now, list down the factors of 772
:1,2,4,193,386,772
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 772,678 . The biggest common factor number is the GCF number.
So the greatest common factor 772,678 is 2.
Lets's calculate LCM of 21,758
Given numbers has no common factors except 1. So, there LCM is their product i.e 15918
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15918
Therefore, the GCF of Fractions 772/21,678/758 is 2/15918
Least Common Multiple of 21,758 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 21,758 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,758) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(21,758) x common factors =1 x 1 = 1
LCM(21,758) = ( 21 × 758 ) / 1
LCM(21,758) = 15918 / 1
LCM(21,758) = 15918
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FAQs on GCF of Fractions of 772/21, 678/758
1. What is the HCF of 772,678?
The HCF of 772,678 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 772/21, 678/758?
Answer: GCF of Numerators as per given numbers 772/21, 678/758 is
GCF of Numerators i.e. for 772,678 is 2
LCM of denominators i.e. for 21,758 is 15918.
Thus, GCF of Fractions is 2/15918.Finally, GCF of Fractions for 772/21, 678/758 is 2/15918.