GCF of 506/680, 524/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 506/680, 524/209 i.e 2/142120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/680, 524/209.
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 506/680,524/209?
Given fractions are 506/680,524/209
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 506/680,524/209, numerators are 506,524
Denominators are 680,209
The GCF of 506,524 is 2 .
LCM of 680,209 is 142120.
The greatest common factor of 506/680,524/209 = [GCF of 506,524]/[LCM of 680,209]= 2/142120
Therefore, the GCF of 506/680,524/209 is 2/142120.
To find the highest common factor of 506,524, we have to find the factors of both numbers and list the highest common factor.
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The factors of 524 are 1, 2, 4, 131, 262, 524
The HCF of 506,524 is 2.
Lets's calculate GCF of 506,524
| 2 | 506, 524 |
| 253, 262 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 506,524 By Matching Biggest Common Factor Method
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Now, list down the factors of 524
:1,2,4,131,262,524
Greatest Common Factor
We found the factors 506,524 . The biggest common factor number is the GCF number.
So the greatest common factor 506,524 is 2.
Lets's calculate LCM of 680,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 142120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/142120
Therefore, the GCF of Fractions 506/680,524/209 is 2/142120
Least Common Multiple of 680,209 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 680,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(680,209) x common factors =1 x 1 = 1
LCM(680,209) = ( 680 × 209 ) / 1
LCM(680,209) = 142120 / 1
LCM(680,209) = 142120
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FAQs on GCF of Fractions of 506/680, 524/209
1. What is the HCF of 506,524?
The HCF of 506,524 is 2
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 506/680, 524/209?
Answer: GCF of Numerators as per given numbers 506/680, 524/209 is
GCF of Numerators i.e. for 506,524 is 2
LCM of denominators i.e. for 680,209 is 142120.
Thus, GCF of Fractions is 2/142120.Finally, GCF of Fractions for 506/680, 524/209 is 2/142120.