GCF of 789/224, 7140/373
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 789/224, 7140/373 i.e 3/83552 easily. The following is the detailed procedure to determine the greatest common factor of fractions 789/224, 7140/373.
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 789/224,7140/373?
Given fractions are 789/224,7140/373
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 789/224,7140/373, numerators are 789,7140
Denominators are 224,373
The GCF of 789,7140 is 3 .
LCM of 224,373 is 83552.
The greatest common factor of 789/224,7140/373 = [GCF of 789,7140]/[LCM of 224,373]= 3/83552
Therefore, the GCF of 789/224,7140/373 is 3/83552.
To find the highest common factor of 789,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 789 are 1, 3, 263, 789
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The HCF of 789,7140 is 3.
Lets's calculate GCF of 789,7140
| 3 | 789, 7140 |
| 263, 2380 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 789,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 789
:1,3,263,789
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Greatest Common Factor
We found the factors 789,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 789,7140 is 3.
Lets's calculate LCM of 224,373
Given numbers has no common factors except 1. So, there LCM is their product i.e 83552
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/83552
Therefore, the GCF of Fractions 789/224,7140/373 is 3/83552
Least Common Multiple of 224,373 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 224,373 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,373) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(224,373) x common factors =1 x 1 = 1
LCM(224,373) = ( 224 × 373 ) / 1
LCM(224,373) = 83552 / 1
LCM(224,373) = 83552
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FAQs on GCF of Fractions of 789/224, 7140/373
1. What is the HCF of 789,7140?
The HCF of 789,7140 is 3
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 789/224, 7140/373?
Answer: GCF of Numerators as per given numbers 789/224, 7140/373 is
GCF of Numerators i.e. for 789,7140 is 3
LCM of denominators i.e. for 224,373 is 83552.
Thus, GCF of Fractions is 3/83552.Finally, GCF of Fractions for 789/224, 7140/373 is 3/83552.