GCF of 509/224, 304/621, 770/826
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 509/224, 304/621, 770/826 i.e 1/8207136 easily. The following is the detailed procedure to determine the greatest common factor of fractions 509/224, 304/621, 770/826.
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 509/224,304/621,770/826?
Given fractions are 509/224,304/621,770/826
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 509/224,304/621,770/826, numerators are 509,304,770
Denominators are 224,621,826
The GCF of 509,304,770 is 1 .
LCM of 224,621,826 is 8207136.
The greatest common factor of 509/224,304/621,770/826 = [GCF of 509,304,770]/[LCM of 224,621,826]= 1/8207136
Therefore, the GCF of 509/224,304/621,770/826 is 1/8207136.
To find the highest common factor of 509,304,770, we have to find the factors of both numbers and list the highest common factor.
The factors of 509 are 1, 509
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770
The HCF of 509,304,770 is 1.
Lets's calculate GCF of 509,304,770
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 509,304,770 By Matching Biggest Common Factor Method
Now, list down the factors of 509
:1,509
Now, list down the factors of 304
:1,2,4,8,16,19,38,76,152,304
Now, list down the factors of 770
:1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770
Greatest Common Factor
We found the factors 509,304,770 . The biggest common factor number is the GCF number.
So the greatest common factor 509,304,770 is 1.
Lets's calculate LCM of 224,621,826
| 2 | 224, 621, 826 |
| 7 | 112, 621, 413 |
| 16, 621, 59 |
∴ So the LCM of the given numbers is 2 x 7 x 16 x 621 x 59 = 8207136
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8207136
Therefore, the GCF of Fractions 509/224,304/621,770/826 is 1/8207136
Least Common Multiple of 224,621,826 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 224,621,826 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(224,621,826) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(224,621,826) x common factors =1 x 14 = 14
LCM(224,621,826) = ( 224 × 621 × 826 ) / 14
LCM(224,621,826) = 114899904 / 14
LCM(224,621,826) = 8207136
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FAQs on GCF of Fractions of 509/224, 304/621, 770/826
1. What is the HCF of 509,304,770?
The HCF of 509,304,770 is 1
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 509/224, 304/621, 770/826?
Answer: GCF of Numerators as per given numbers 509/224, 304/621, 770/826 is
GCF of Numerators i.e. for 509,304,770 is 1
LCM of denominators i.e. for 224,621,826 is 8207136.
Thus, GCF of Fractions is 1/8207136.Finally, GCF of Fractions for 509/224, 304/621, 770/826 is 1/8207136.