GCF of 7722/195, 5040/5609
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7722/195, 5040/5609 i.e 18/1093755 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7722/195, 5040/5609.
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 7722/195,5040/5609?
Given fractions are 7722/195,5040/5609
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 7722/195,5040/5609, numerators are 7722,5040
Denominators are 195,5609
The GCF of 7722,5040 is 18 .
LCM of 195,5609 is 1093755.
The greatest common factor of 7722/195,5040/5609 = [GCF of 7722,5040]/[LCM of 195,5609]= 18/1093755
Therefore, the GCF of 7722/195,5040/5609 is 18/1093755.
To find the highest common factor of 7722,5040, we have to find the factors of both numbers and list the highest common factor.
The factors of 7722 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 27, 33, 39, 54, 66, 78, 99, 117, 143, 198, 234, 286, 297, 351, 429, 594, 702, 858, 1287, 2574, 3861, 7722
The factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040
The HCF of 7722,5040 is 18.
Lets's calculate GCF of 7722,5040
| 2 | 7722, 5040 |
| 3 | 3861, 2520 |
| 3 | 1287, 840 |
| 429, 280 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 7722,5040 By Matching Biggest Common Factor Method
Now, list down the factors of 7722
:1,2,3,6,9,11,13,18,22,26,27,33,39,54,66,78,99,117,143,198,234,286,297,351,429,594,702,858,1287,2574,3861,7722
Now, list down the factors of 5040
:1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,28,30,35,36,40,42,45,48,56,60,63,70,72,80,84,90,105,112,120,126,140,144,168,180,210,240,252,280,315,336,360,420,504,560,630,720,840,1008,1260,1680,2520,5040
Greatest Common Factor
We found the factors 7722,5040 . The biggest common factor number is the GCF number.
So the greatest common factor 7722,5040 is 18.
Lets's calculate LCM of 195,5609
Given numbers has no common factors except 1. So, there LCM is their product i.e 1093755
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/1093755
Therefore, the GCF of Fractions 7722/195,5040/5609 is 18/1093755
Least Common Multiple of 195,5609 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 195,5609 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(195,5609) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(195,5609) x common factors =1 x 1 = 1
LCM(195,5609) = ( 195 × 5609 ) / 1
LCM(195,5609) = 1093755 / 1
LCM(195,5609) = 1093755
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FAQs on GCF of Fractions of 7722/195, 5040/5609
1. What is the HCF of 7722,5040?
The HCF of 7722,5040 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 7722/195, 5040/5609?
Answer: GCF of Numerators as per given numbers 7722/195, 5040/5609 is
GCF of Numerators i.e. for 7722,5040 is 18
LCM of denominators i.e. for 195,5609 is 1093755.
Thus, GCF of Fractions is 18/1093755.Finally, GCF of Fractions for 7722/195, 5040/5609 is 18/1093755.