GCF of 2775/305, 7140/8470
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2775/305, 7140/8470 i.e 15/516670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2775/305, 7140/8470.
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 2775/305,7140/8470?
Given fractions are 2775/305,7140/8470
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 2775/305,7140/8470, numerators are 2775,7140
Denominators are 305,8470
The GCF of 2775,7140 is 15 .
LCM of 305,8470 is 516670.
The greatest common factor of 2775/305,7140/8470 = [GCF of 2775,7140]/[LCM of 305,8470]= 15/516670
Therefore, the GCF of 2775/305,7140/8470 is 15/516670.
To find the highest common factor of 2775,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 2775 are 1, 3, 5, 15, 25, 37, 75, 111, 185, 555, 925, 2775
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 2775,7140 is 15.
Lets's calculate GCF of 2775,7140
| 3 | 2775, 7140 |
| 5 | 925, 2380 |
| 185, 476 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 2775,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 2775
:1,3,5,15,25,37,75,111,185,555,925,2775
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 2775,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 2775,7140 is 15.
Lets's calculate LCM of 305,8470
| 5 | 305, 8470 |
| 61, 1694 |
∴ So the LCM of the given numbers is 5 x 61 x 1694 = 516670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/516670
Therefore, the GCF of Fractions 2775/305,7140/8470 is 15/516670
Least Common Multiple of 305,8470 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 305,8470 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,8470) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(305,8470) x common factors =5 x 1 = 5
LCM(305,8470) = ( 305 × 8470 ) / 5
LCM(305,8470) = 2583350 / 5
LCM(305,8470) = 516670
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 2775/305, 7140/8470
1. What is the HCF of 2775,7140?
The HCF of 2775,7140 is 15
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 2775/305, 7140/8470?
Answer: GCF of Numerators as per given numbers 2775/305, 7140/8470 is
GCF of Numerators i.e. for 2775,7140 is 15
LCM of denominators i.e. for 305,8470 is 516670.
Thus, GCF of Fractions is 15/516670.Finally, GCF of Fractions for 2775/305, 7140/8470 is 15/516670.