GCF of 77/31, 189/66, 880/456
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 77/31, 189/66, 880/456 i.e 1/155496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/31, 189/66, 880/456.
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 77/31,189/66,880/456?
Given fractions are 77/31,189/66,880/456
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 77/31,189/66,880/456, numerators are 77,189,880
Denominators are 31,66,456
The GCF of 77,189,880 is 1 .
LCM of 31,66,456 is 155496.
The greatest common factor of 77/31,189/66,880/456 = [GCF of 77,189,880]/[LCM of 31,66,456]= 1/155496
Therefore, the GCF of 77/31,189/66,880/456 is 1/155496.
To find the highest common factor of 77,189,880, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The factors of 880 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880
The HCF of 77,189,880 is 1.
Lets's calculate GCF of 77,189,880
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 77,189,880 By Matching Biggest Common Factor Method
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Now, list down the factors of 880
:1,2,4,5,8,10,11,16,20,22,40,44,55,80,88,110,176,220,440,880
Greatest Common Factor
We found the factors 77,189,880 . The biggest common factor number is the GCF number.
So the greatest common factor 77,189,880 is 1.
Lets's calculate LCM of 31,66,456
| 2 | 31, 66, 456 |
| 3 | 31, 33, 228 |
| 31, 11, 76 |
∴ So the LCM of the given numbers is 2 x 3 x 31 x 11 x 76 = 155496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/155496
Therefore, the GCF of Fractions 77/31,189/66,880/456 is 1/155496
Least Common Multiple of 31,66,456 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 31,66,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,66,456) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(31,66,456) x common factors =1 x 6 = 6
LCM(31,66,456) = ( 31 × 66 × 456 ) / 6
LCM(31,66,456) = 932976 / 6
LCM(31,66,456) = 155496
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FAQs on GCF of Fractions of 77/31, 189/66, 880/456
1. What is the HCF of 77,189,880?
The HCF of 77,189,880 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 77/31, 189/66, 880/456?
Answer: GCF of Numerators as per given numbers 77/31, 189/66, 880/456 is
GCF of Numerators i.e. for 77,189,880 is 1
LCM of denominators i.e. for 31,66,456 is 155496.
Thus, GCF of Fractions is 1/155496.Finally, GCF of Fractions for 77/31, 189/66, 880/456 is 1/155496.