GCF of 357/420, 292/706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 357/420, 292/706 i.e 1/148260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 357/420, 292/706.
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 357/420,292/706?
Given fractions are 357/420,292/706
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 357/420,292/706, numerators are 357,292
Denominators are 420,706
The GCF of 357,292 is 1 .
LCM of 420,706 is 148260.
The greatest common factor of 357/420,292/706 = [GCF of 357,292]/[LCM of 420,706]= 1/148260
Therefore, the GCF of 357/420,292/706 is 1/148260.
To find the highest common factor of 357,292, we have to find the factors of both numbers and list the highest common factor.
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357
The factors of 292 are 1, 2, 4, 73, 146, 292
The HCF of 357,292 is 1.
Lets's calculate GCF of 357,292
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 357,292 By Matching Biggest Common Factor Method
Now, list down the factors of 357
:1,3,7,17,21,51,119,357
Now, list down the factors of 292
:1,2,4,73,146,292
Greatest Common Factor
We found the factors 357,292 . The biggest common factor number is the GCF number.
So the greatest common factor 357,292 is 1.
Lets's calculate LCM of 420,706
| 2 | 420, 706 |
| 210, 353 |
∴ So the LCM of the given numbers is 2 x 210 x 353 = 148260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/148260
Therefore, the GCF of Fractions 357/420,292/706 is 1/148260
Least Common Multiple of 420,706 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 420,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,706) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(420,706) x common factors =2 x 1 = 2
LCM(420,706) = ( 420 × 706 ) / 2
LCM(420,706) = 296520 / 2
LCM(420,706) = 148260
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FAQs on GCF of Fractions of 357/420, 292/706
1. What is the HCF of 357,292?
The HCF of 357,292 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 357/420, 292/706?
Answer: GCF of Numerators as per given numbers 357/420, 292/706 is
GCF of Numerators i.e. for 357,292 is 1
LCM of denominators i.e. for 420,706 is 148260.
Thus, GCF of Fractions is 1/148260.Finally, GCF of Fractions for 357/420, 292/706 is 1/148260.