GCF of 702/785, 8172/1585
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 702/785, 8172/1585 i.e 18/248845 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/785, 8172/1585.
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 702/785,8172/1585?
Given fractions are 702/785,8172/1585
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 702/785,8172/1585, numerators are 702,8172
Denominators are 785,1585
The GCF of 702,8172 is 18 .
LCM of 785,1585 is 248845.
The greatest common factor of 702/785,8172/1585 = [GCF of 702,8172]/[LCM of 785,1585]= 18/248845
Therefore, the GCF of 702/785,8172/1585 is 18/248845.
To find the highest common factor of 702,8172, we have to find the factors of both numbers and list the highest common factor.
The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The factors of 8172 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 227, 454, 681, 908, 1362, 2043, 2724, 4086, 8172
The HCF of 702,8172 is 18.
Lets's calculate GCF of 702,8172
| 2 | 702, 8172 |
| 3 | 351, 4086 |
| 3 | 117, 1362 |
| 39, 454 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 702,8172 By Matching Biggest Common Factor Method
Now, list down the factors of 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Now, list down the factors of 8172
:1,2,3,4,6,9,12,18,36,227,454,681,908,1362,2043,2724,4086,8172
Greatest Common Factor
We found the factors 702,8172 . The biggest common factor number is the GCF number.
So the greatest common factor 702,8172 is 18.
Lets's calculate LCM of 785,1585
| 5 | 785, 1585 |
| 157, 317 |
∴ So the LCM of the given numbers is 5 x 157 x 317 = 248845
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/248845
Therefore, the GCF of Fractions 702/785,8172/1585 is 18/248845
Least Common Multiple of 785,1585 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 785,1585 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(785,1585) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(785,1585) x common factors =5 x 1 = 5
LCM(785,1585) = ( 785 × 1585 ) / 5
LCM(785,1585) = 1244225 / 5
LCM(785,1585) = 248845
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FAQs on GCF of Fractions of 702/785, 8172/1585
1. What is the HCF of 702,8172?
The HCF of 702,8172 is 18
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 702/785, 8172/1585?
Answer: GCF of Numerators as per given numbers 702/785, 8172/1585 is
GCF of Numerators i.e. for 702,8172 is 18
LCM of denominators i.e. for 785,1585 is 248845.
Thus, GCF of Fractions is 18/248845.Finally, GCF of Fractions for 702/785, 8172/1585 is 18/248845.