GCF of 82/64, 46/78, 42/64, 68/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/64, 46/78, 42/64, 68/31 i.e 2/77376 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/64, 46/78, 42/64, 68/31.
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 82/64,46/78,42/64,68/31?
Given fractions are 82/64,46/78,42/64,68/31
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 82/64,46/78,42/64,68/31, numerators are 82,46,42,68
Denominators are 64,78,64,31
The GCF of 82,46,42,68 is 2 .
LCM of 64,78,64,31 is 77376.
The greatest common factor of 82/64,46/78,42/64,68/31 = [GCF of 82,46,42,68]/[LCM of 64,78,64,31]= 2/77376
Therefore, the GCF of 82/64,46/78,42/64,68/31 is 2/77376.
To find the highest common factor of 82,46,42,68, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 46 are 1, 2, 23, 46
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 68 are 1, 2, 4, 17, 34, 68
The HCF of 82,46,42,68 is 2.
Lets's calculate GCF of 82,46,42,68
| 2 | 82, 46, 42, 68 |
| 41, 23, 21, 34 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 82,46,42,68 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 68
:1,2,4,17,34,68
Greatest Common Factor
We found the factors 82,46,42,68 . The biggest common factor number is the GCF number.
So the greatest common factor 82,46,42,68 is 2.
Lets's calculate LCM of 64,78,64,31
| 2 | 64, 78, 64, 31 |
| 2 | 32, 39, 32, 31 |
| 2 | 16, 39, 16, 31 |
| 2 | 8, 39, 8, 31 |
| 2 | 4, 39, 4, 31 |
| 2 | 2, 39, 2, 31 |
| 1, 39, 1, 31 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 1 x 39 x 1 x 31 = 77376
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/77376
Therefore, the GCF of Fractions 82/64,46/78,42/64,68/31 is 2/77376
Least Common Multiple of 64,78,64,31 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 64,78,64,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,78,64,31) = 1
common factors(in case of two or more numbers have common factors) = 128
GCF(64,78,64,31) x common factors =1 x 128 = 128
LCM(64,78,64,31) = ( 64 × 78 × 64 × 31 ) / 128
LCM(64,78,64,31) = 9904128 / 128
LCM(64,78,64,31) = 77376
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 82/64, 46/78, 42/64, 68/31
1. What is the HCF of 82,46,42,68?
The HCF of 82,46,42,68 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 82/64, 46/78, 42/64, 68/31?
Answer: GCF of Numerators as per given numbers 82/64, 46/78, 42/64, 68/31 is
GCF of Numerators i.e. for 82,46,42,68 is 2
LCM of denominators i.e. for 64,78,64,31 is 77376.
Thus, GCF of Fractions is 2/77376.Finally, GCF of Fractions for 82/64, 46/78, 42/64, 68/31 is 2/77376.