GCF of 61/78, 708/16, 688/965
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 61/78, 708/16, 688/965 i.e 1/602160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/78, 708/16, 688/965.
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 61/78,708/16,688/965?
Given fractions are 61/78,708/16,688/965
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 61/78,708/16,688/965, numerators are 61,708,688
Denominators are 78,16,965
The GCF of 61,708,688 is 1 .
LCM of 78,16,965 is 602160.
The greatest common factor of 61/78,708/16,688/965 = [GCF of 61,708,688]/[LCM of 78,16,965]= 1/602160
Therefore, the GCF of 61/78,708/16,688/965 is 1/602160.
To find the highest common factor of 61,708,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 61 are 1, 61
The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 61,708,688 is 1.
Lets's calculate GCF of 61,708,688
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 61,708,688 By Matching Biggest Common Factor Method
Now, list down the factors of 61
:1,61
Now, list down the factors of 708
:1,2,3,4,6,12,59,118,177,236,354,708
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 61,708,688 . The biggest common factor number is the GCF number.
So the greatest common factor 61,708,688 is 1.
Lets's calculate LCM of 78,16,965
| 2 | 78, 16, 965 |
| 39, 8, 965 |
∴ So the LCM of the given numbers is 2 x 39 x 8 x 965 = 602160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/602160
Therefore, the GCF of Fractions 61/78,708/16,688/965 is 1/602160
Least Common Multiple of 78,16,965 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 78,16,965 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,16,965) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(78,16,965) x common factors =1 x 2 = 2
LCM(78,16,965) = ( 78 × 16 × 965 ) / 2
LCM(78,16,965) = 1204320 / 2
LCM(78,16,965) = 602160
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FAQs on GCF of Fractions of 61/78, 708/16, 688/965
1. What is the HCF of 61,708,688?
The HCF of 61,708,688 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 61/78, 708/16, 688/965?
Answer: GCF of Numerators as per given numbers 61/78, 708/16, 688/965 is
GCF of Numerators i.e. for 61,708,688 is 1
LCM of denominators i.e. for 78,16,965 is 602160.
Thus, GCF of Fractions is 1/602160.Finally, GCF of Fractions for 61/78, 708/16, 688/965 is 1/602160.