GCF of 2320/429, 7840/306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2320/429, 7840/306 i.e 80/43758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2320/429, 7840/306.
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 2320/429,7840/306?
Given fractions are 2320/429,7840/306
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 2320/429,7840/306, numerators are 2320,7840
Denominators are 429,306
The GCF of 2320,7840 is 80 .
LCM of 429,306 is 43758.
The greatest common factor of 2320/429,7840/306 = [GCF of 2320,7840]/[LCM of 429,306]= 80/43758
Therefore, the GCF of 2320/429,7840/306 is 80/43758.
To find the highest common factor of 2320,7840, we have to find the factors of both numbers and list the highest common factor.
The factors of 2320 are 1, 2, 4, 5, 8, 10, 16, 20, 29, 40, 58, 80, 116, 145, 232, 290, 464, 580, 1160, 2320
The factors of 7840 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 49, 56, 70, 80, 98, 112, 140, 160, 196, 224, 245, 280, 392, 490, 560, 784, 980, 1120, 1568, 1960, 3920, 7840
The HCF of 2320,7840 is 80.
Lets's calculate GCF of 2320,7840
| 2 | 2320, 7840 |
| 2 | 1160, 3920 |
| 2 | 580, 1960 |
| 2 | 290, 980 |
| 5 | 145, 490 |
| 29, 98 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 5 = 80
Greatest Common Factor of 2320,7840 By Matching Biggest Common Factor Method
Now, list down the factors of 2320
:1,2,4,5,8,10,16,20,29,40,58,80,116,145,232,290,464,580,1160,2320
Now, list down the factors of 7840
:1,2,4,5,7,8,10,14,16,20,28,32,35,40,49,56,70,80,98,112,140,160,196,224,245,280,392,490,560,784,980,1120,1568,1960,3920,7840
Greatest Common Factor
We found the factors 2320,7840 . The biggest common factor number is the GCF number.
So the greatest common factor 2320,7840 is 80.
Lets's calculate LCM of 429,306
| 3 | 429, 306 |
| 143, 102 |
∴ So the LCM of the given numbers is 3 x 143 x 102 = 43758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 80/43758
Therefore, the GCF of Fractions 2320/429,7840/306 is 80/43758
Least Common Multiple of 429,306 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 429,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(429,306) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(429,306) x common factors =3 x 1 = 3
LCM(429,306) = ( 429 × 306 ) / 3
LCM(429,306) = 131274 / 3
LCM(429,306) = 43758
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FAQs on GCF of Fractions of 2320/429, 7840/306
1. What is the HCF of 2320,7840?
The HCF of 2320,7840 is 80
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 2320/429, 7840/306?
Answer: GCF of Numerators as per given numbers 2320/429, 7840/306 is
GCF of Numerators i.e. for 2320,7840 is 80
LCM of denominators i.e. for 429,306 is 43758.
Thus, GCF of Fractions is 80/43758.Finally, GCF of Fractions for 2320/429, 7840/306 is 80/43758.