GCF of 785/72, 531/51, 102/77
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 785/72, 531/51, 102/77 i.e 1/94248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 785/72, 531/51, 102/77.
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 785/72,531/51,102/77?
Given fractions are 785/72,531/51,102/77
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 785/72,531/51,102/77, numerators are 785,531,102
Denominators are 72,51,77
The GCF of 785,531,102 is 1 .
LCM of 72,51,77 is 94248.
The greatest common factor of 785/72,531/51,102/77 = [GCF of 785,531,102]/[LCM of 72,51,77]= 1/94248
Therefore, the GCF of 785/72,531/51,102/77 is 1/94248.
To find the highest common factor of 785,531,102, we have to find the factors of both numbers and list the highest common factor.
The factors of 785 are 1, 5, 157, 785
The factors of 531 are 1, 3, 9, 59, 177, 531
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The HCF of 785,531,102 is 1.
Lets's calculate GCF of 785,531,102
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 785,531,102 By Matching Biggest Common Factor Method
Now, list down the factors of 785
:1,5,157,785
Now, list down the factors of 531
:1,3,9,59,177,531
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Greatest Common Factor
We found the factors 785,531,102 . The biggest common factor number is the GCF number.
So the greatest common factor 785,531,102 is 1.
Lets's calculate LCM of 72,51,77
| 3 | 72, 51, 77 |
| 24, 17, 77 |
∴ So the LCM of the given numbers is 3 x 24 x 17 x 77 = 94248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/94248
Therefore, the GCF of Fractions 785/72,531/51,102/77 is 1/94248
Least Common Multiple of 72,51,77 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 72,51,77 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,51,77) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(72,51,77) x common factors =1 x 3 = 3
LCM(72,51,77) = ( 72 × 51 × 77 ) / 3
LCM(72,51,77) = 282744 / 3
LCM(72,51,77) = 94248
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FAQs on GCF of Fractions of 785/72, 531/51, 102/77
1. What is the HCF of 785,531,102?
The HCF of 785,531,102 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 785/72, 531/51, 102/77?
Answer: GCF of Numerators as per given numbers 785/72, 531/51, 102/77 is
GCF of Numerators i.e. for 785,531,102 is 1
LCM of denominators i.e. for 72,51,77 is 94248.
Thus, GCF of Fractions is 1/94248.Finally, GCF of Fractions for 785/72, 531/51, 102/77 is 1/94248.