GCF of 7630/168, 6540/1638
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7630/168, 6540/1638 i.e 1090/6552 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7630/168, 6540/1638.
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 7630/168,6540/1638?
Given fractions are 7630/168,6540/1638
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 7630/168,6540/1638, numerators are 7630,6540
Denominators are 168,1638
The GCF of 7630,6540 is 1090 .
LCM of 168,1638 is 6552.
The greatest common factor of 7630/168,6540/1638 = [GCF of 7630,6540]/[LCM of 168,1638]= 1090/6552
Therefore, the GCF of 7630/168,6540/1638 is 1090/6552.
To find the highest common factor of 7630,6540, we have to find the factors of both numbers and list the highest common factor.
The factors of 7630 are 1, 2, 5, 7, 10, 14, 35, 70, 109, 218, 545, 763, 1090, 1526, 3815, 7630
The factors of 6540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 109, 218, 327, 436, 545, 654, 1090, 1308, 1635, 2180, 3270, 6540
The HCF of 7630,6540 is 1090.
Lets's calculate GCF of 7630,6540
| 2 | 7630, 6540 |
| 5 | 3815, 3270 |
| 109 | 763, 654 |
| 7, 6 |
∴ So the GCF of the given numbers is 2 x 5 x 109 = 1090
Greatest Common Factor of 7630,6540 By Matching Biggest Common Factor Method
Now, list down the factors of 7630
:1,2,5,7,10,14,35,70,109,218,545,763,1090,1526,3815,7630
Now, list down the factors of 6540
:1,2,3,4,5,6,10,12,15,20,30,60,109,218,327,436,545,654,1090,1308,1635,2180,3270,6540
Greatest Common Factor
We found the factors 7630,6540 . The biggest common factor number is the GCF number.
So the greatest common factor 7630,6540 is 1090.
Lets's calculate LCM of 168,1638
| 2 | 168, 1638 |
| 3 | 84, 819 |
| 7 | 28, 273 |
| 4, 39 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 4 x 39 = 6552
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1090/6552
Therefore, the GCF of Fractions 7630/168,6540/1638 is 1090/6552
Least Common Multiple of 168,1638 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 168,1638 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(168,1638) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(168,1638) x common factors =42 x 1 = 42
LCM(168,1638) = ( 168 × 1638 ) / 42
LCM(168,1638) = 275184 / 42
LCM(168,1638) = 6552
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7630/168, 6540/1638
1. What is the HCF of 7630,6540?
The HCF of 7630,6540 is 1090
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 7630/168, 6540/1638?
Answer: GCF of Numerators as per given numbers 7630/168, 6540/1638 is
GCF of Numerators i.e. for 7630,6540 is 1090
LCM of denominators i.e. for 168,1638 is 6552.
Thus, GCF of Fractions is 1090/6552.Finally, GCF of Fractions for 7630/168, 6540/1638 is 1090/6552.