GCF of 14/77, 77/23, 364/644
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/77, 77/23, 364/644 i.e 7/7084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/77, 77/23, 364/644.
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 14/77,77/23,364/644?
Given fractions are 14/77,77/23,364/644
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 14/77,77/23,364/644, numerators are 14,77,364
Denominators are 77,23,644
The GCF of 14,77,364 is 7 .
LCM of 77,23,644 is 7084.
The greatest common factor of 14/77,77/23,364/644 = [GCF of 14,77,364]/[LCM of 77,23,644]= 7/7084
Therefore, the GCF of 14/77,77/23,364/644 is 7/7084.
To find the highest common factor of 14,77,364, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 77 are 1, 7, 11, 77
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The HCF of 14,77,364 is 7.
Lets's calculate GCF of 14,77,364
| 7 | 14, 77, 364 |
| 2, 11, 52 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 14,77,364 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Greatest Common Factor
We found the factors 14,77,364 . The biggest common factor number is the GCF number.
So the greatest common factor 14,77,364 is 7.
Lets's calculate LCM of 77,23,644
| 7 | 77, 23, 644 |
| 23 | 11, 23, 92 |
| 11, 1, 4 |
∴ So the LCM of the given numbers is 7 x 23 x 11 x 1 x 4 = 7084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/7084
Therefore, the GCF of Fractions 14/77,77/23,364/644 is 7/7084
Least Common Multiple of 77,23,644 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 77,23,644 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,23,644) = 1
common factors(in case of two or more numbers have common factors) = 161
GCF(77,23,644) x common factors =1 x 161 = 161
LCM(77,23,644) = ( 77 × 23 × 644 ) / 161
LCM(77,23,644) = 1140524 / 161
LCM(77,23,644) = 7084
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FAQs on GCF of Fractions of 14/77, 77/23, 364/644
1. What is the HCF of 14,77,364?
The HCF of 14,77,364 is 7
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 14/77, 77/23, 364/644?
Answer: GCF of Numerators as per given numbers 14/77, 77/23, 364/644 is
GCF of Numerators i.e. for 14,77,364 is 7
LCM of denominators i.e. for 77,23,644 is 7084.
Thus, GCF of Fractions is 7/7084.Finally, GCF of Fractions for 14/77, 77/23, 364/644 is 7/7084.