GCF of 7220/717, 7410/7854
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7220/717, 7410/7854 i.e 190/1877106 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7220/717, 7410/7854.
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 7220/717,7410/7854?
Given fractions are 7220/717,7410/7854
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 7220/717,7410/7854, numerators are 7220,7410
Denominators are 717,7854
The GCF of 7220,7410 is 190 .
LCM of 717,7854 is 1877106.
The greatest common factor of 7220/717,7410/7854 = [GCF of 7220,7410]/[LCM of 717,7854]= 190/1877106
Therefore, the GCF of 7220/717,7410/7854 is 190/1877106.
To find the highest common factor of 7220,7410, we have to find the factors of both numbers and list the highest common factor.
The factors of 7220 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 361, 380, 722, 1444, 1805, 3610, 7220
The factors of 7410 are 1, 2, 3, 5, 6, 10, 13, 15, 19, 26, 30, 38, 39, 57, 65, 78, 95, 114, 130, 190, 195, 247, 285, 390, 494, 570, 741, 1235, 1482, 2470, 3705, 7410
The HCF of 7220,7410 is 190.
Lets's calculate GCF of 7220,7410
| 2 | 7220, 7410 |
| 5 | 3610, 3705 |
| 19 | 722, 741 |
| 38, 39 |
∴ So the GCF of the given numbers is 2 x 5 x 19 = 190
Greatest Common Factor of 7220,7410 By Matching Biggest Common Factor Method
Now, list down the factors of 7220
:1,2,4,5,10,19,20,38,76,95,190,361,380,722,1444,1805,3610,7220
Now, list down the factors of 7410
:1,2,3,5,6,10,13,15,19,26,30,38,39,57,65,78,95,114,130,190,195,247,285,390,494,570,741,1235,1482,2470,3705,7410
Greatest Common Factor
We found the factors 7220,7410 . The biggest common factor number is the GCF number.
So the greatest common factor 7220,7410 is 190.
Lets's calculate LCM of 717,7854
| 3 | 717, 7854 |
| 239, 2618 |
∴ So the LCM of the given numbers is 3 x 239 x 2618 = 1877106
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 190/1877106
Therefore, the GCF of Fractions 7220/717,7410/7854 is 190/1877106
Least Common Multiple of 717,7854 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 717,7854 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(717,7854) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(717,7854) x common factors =3 x 1 = 3
LCM(717,7854) = ( 717 × 7854 ) / 3
LCM(717,7854) = 5631318 / 3
LCM(717,7854) = 1877106
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FAQs on GCF of Fractions of 7220/717, 7410/7854
1. What is the HCF of 7220,7410?
The HCF of 7220,7410 is 190
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 7220/717, 7410/7854?
Answer: GCF of Numerators as per given numbers 7220/717, 7410/7854 is
GCF of Numerators i.e. for 7220,7410 is 190
LCM of denominators i.e. for 717,7854 is 1877106.
Thus, GCF of Fractions is 190/1877106.Finally, GCF of Fractions for 7220/717, 7410/7854 is 190/1877106.