GCF of 780/706, 690/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 780/706, 690/218 i.e 30/76954 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/706, 690/218.
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 780/706,690/218?
Given fractions are 780/706,690/218
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 780/706,690/218, numerators are 780,690
Denominators are 706,218
The GCF of 780,690 is 30 .
LCM of 706,218 is 76954.
The greatest common factor of 780/706,690/218 = [GCF of 780,690]/[LCM of 706,218]= 30/76954
Therefore, the GCF of 780/706,690/218 is 30/76954.
To find the highest common factor of 780,690, we have to find the factors of both numbers and list the highest common factor.
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The HCF of 780,690 is 30.
Lets's calculate GCF of 780,690
| 2 | 780, 690 |
| 3 | 390, 345 |
| 5 | 130, 115 |
| 26, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 780,690 By Matching Biggest Common Factor Method
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Greatest Common Factor
We found the factors 780,690 . The biggest common factor number is the GCF number.
So the greatest common factor 780,690 is 30.
Lets's calculate LCM of 706,218
| 2 | 706, 218 |
| 353, 109 |
∴ So the LCM of the given numbers is 2 x 353 x 109 = 76954
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/76954
Therefore, the GCF of Fractions 780/706,690/218 is 30/76954
Least Common Multiple of 706,218 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 706,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(706,218) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(706,218) x common factors =2 x 1 = 2
LCM(706,218) = ( 706 × 218 ) / 2
LCM(706,218) = 153908 / 2
LCM(706,218) = 76954
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FAQs on GCF of Fractions of 780/706, 690/218
1. What is the HCF of 780,690?
The HCF of 780,690 is 30
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 780/706, 690/218?
Answer: GCF of Numerators as per given numbers 780/706, 690/218 is
GCF of Numerators i.e. for 780,690 is 30
LCM of denominators i.e. for 706,218 is 76954.
Thus, GCF of Fractions is 30/76954.Finally, GCF of Fractions for 780/706, 690/218 is 30/76954.