GCF of 287/221, 7980/102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 287/221, 7980/102 i.e 7/1326 easily. The following is the detailed procedure to determine the greatest common factor of fractions 287/221, 7980/102.
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 287/221,7980/102?
Given fractions are 287/221,7980/102
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 287/221,7980/102, numerators are 287,7980
Denominators are 221,102
The GCF of 287,7980 is 7 .
LCM of 221,102 is 1326.
The greatest common factor of 287/221,7980/102 = [GCF of 287,7980]/[LCM of 221,102]= 7/1326
Therefore, the GCF of 287/221,7980/102 is 7/1326.
To find the highest common factor of 287,7980, we have to find the factors of both numbers and list the highest common factor.
The factors of 287 are 1, 7, 41, 287
The factors of 7980 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 19, 20, 21, 28, 30, 35, 38, 42, 57, 60, 70, 76, 84, 95, 105, 114, 133, 140, 190, 210, 228, 266, 285, 380, 399, 420, 532, 570, 665, 798, 1140, 1330, 1596, 1995, 2660, 3990, 7980
The HCF of 287,7980 is 7.
Lets's calculate GCF of 287,7980
| 7 | 287, 7980 |
| 41, 1140 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 287,7980 By Matching Biggest Common Factor Method
Now, list down the factors of 287
:1,7,41,287
Now, list down the factors of 7980
:1,2,3,4,5,6,7,10,12,14,15,19,20,21,28,30,35,38,42,57,60,70,76,84,95,105,114,133,140,190,210,228,266,285,380,399,420,532,570,665,798,1140,1330,1596,1995,2660,3990,7980
Greatest Common Factor
We found the factors 287,7980 . The biggest common factor number is the GCF number.
So the greatest common factor 287,7980 is 7.
Lets's calculate LCM of 221,102
| 17 | 221, 102 |
| 13, 6 |
∴ So the LCM of the given numbers is 17 x 13 x 6 = 1326
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/1326
Therefore, the GCF of Fractions 287/221,7980/102 is 7/1326
Least Common Multiple of 221,102 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 221,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(221,102) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(221,102) x common factors =17 x 1 = 17
LCM(221,102) = ( 221 × 102 ) / 17
LCM(221,102) = 22542 / 17
LCM(221,102) = 1326
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FAQs on GCF of Fractions of 287/221, 7980/102
1. What is the HCF of 287,7980?
The HCF of 287,7980 is 7
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 287/221, 7980/102?
Answer: GCF of Numerators as per given numbers 287/221, 7980/102 is
GCF of Numerators i.e. for 287,7980 is 7
LCM of denominators i.e. for 221,102 is 1326.
Thus, GCF of Fractions is 7/1326.Finally, GCF of Fractions for 287/221, 7980/102 is 7/1326.