GCF of 506/105, 374/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 506/105, 374/686 i.e 22/10290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/105, 374/686.
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 506/105,374/686?
Given fractions are 506/105,374/686
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 506/105,374/686, numerators are 506,374
Denominators are 105,686
The GCF of 506,374 is 22 .
LCM of 105,686 is 10290.
The greatest common factor of 506/105,374/686 = [GCF of 506,374]/[LCM of 105,686]= 22/10290
Therefore, the GCF of 506/105,374/686 is 22/10290.
To find the highest common factor of 506,374, 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 374 are 1, 2, 11, 17, 22, 34, 187, 374
The HCF of 506,374 is 22.
Lets's calculate GCF of 506,374
| 2 | 506, 374 |
| 11 | 253, 187 |
| 23, 17 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 506,374 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 374
:1,2,11,17,22,34,187,374
Greatest Common Factor
We found the factors 506,374 . The biggest common factor number is the GCF number.
So the greatest common factor 506,374 is 22.
Lets's calculate LCM of 105,686
| 7 | 105, 686 |
| 15, 98 |
∴ So the LCM of the given numbers is 7 x 15 x 98 = 10290
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/10290
Therefore, the GCF of Fractions 506/105,374/686 is 22/10290
Least Common Multiple of 105,686 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 105,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,686) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(105,686) x common factors =7 x 1 = 7
LCM(105,686) = ( 105 × 686 ) / 7
LCM(105,686) = 72030 / 7
LCM(105,686) = 10290
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FAQs on GCF of Fractions of 506/105, 374/686
1. What is the HCF of 506,374?
The HCF of 506,374 is 22
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 506/105, 374/686?
Answer: GCF of Numerators as per given numbers 506/105, 374/686 is
GCF of Numerators i.e. for 506,374 is 22
LCM of denominators i.e. for 105,686 is 10290.
Thus, GCF of Fractions is 22/10290.Finally, GCF of Fractions for 506/105, 374/686 is 22/10290.