GCF of 297/207, 780/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 297/207, 780/409 i.e 3/84663 easily. The following is the detailed procedure to determine the greatest common factor of fractions 297/207, 780/409.
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 297/207,780/409?
Given fractions are 297/207,780/409
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 297/207,780/409, numerators are 297,780
Denominators are 207,409
The GCF of 297,780 is 3 .
LCM of 207,409 is 84663.
The greatest common factor of 297/207,780/409 = [GCF of 297,780]/[LCM of 207,409]= 3/84663
Therefore, the GCF of 297/207,780/409 is 3/84663.
To find the highest common factor of 297,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 297 are 1, 3, 9, 11, 27, 33, 99, 297
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 HCF of 297,780 is 3.
Lets's calculate GCF of 297,780
| 3 | 297, 780 |
| 99, 260 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 297,780 By Matching Biggest Common Factor Method
Now, list down the factors of 297
:1,3,9,11,27,33,99,297
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
Greatest Common Factor
We found the factors 297,780 . The biggest common factor number is the GCF number.
So the greatest common factor 297,780 is 3.
Lets's calculate LCM of 207,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 84663
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/84663
Therefore, the GCF of Fractions 297/207,780/409 is 3/84663
Least Common Multiple of 207,409 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 207,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(207,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(207,409) x common factors =1 x 1 = 1
LCM(207,409) = ( 207 × 409 ) / 1
LCM(207,409) = 84663 / 1
LCM(207,409) = 84663
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FAQs on GCF of Fractions of 297/207, 780/409
1. What is the HCF of 297,780?
The HCF of 297,780 is 3
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 297/207, 780/409?
Answer: GCF of Numerators as per given numbers 297/207, 780/409 is
GCF of Numerators i.e. for 297,780 is 3
LCM of denominators i.e. for 207,409 is 84663.
Thus, GCF of Fractions is 3/84663.Finally, GCF of Fractions for 297/207, 780/409 is 3/84663.