GCF of 421/535, 978/705
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 421/535, 978/705 i.e 1/75435 easily. The following is the detailed procedure to determine the greatest common factor of fractions 421/535, 978/705.
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 421/535,978/705?
Given fractions are 421/535,978/705
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 421/535,978/705, numerators are 421,978
Denominators are 535,705
The GCF of 421,978 is 1 .
LCM of 535,705 is 75435.
The greatest common factor of 421/535,978/705 = [GCF of 421,978]/[LCM of 535,705]= 1/75435
Therefore, the GCF of 421/535,978/705 is 1/75435.
To find the highest common factor of 421,978, we have to find the factors of both numbers and list the highest common factor.
The factors of 421 are 1, 421
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The HCF of 421,978 is 1.
Lets's calculate GCF of 421,978
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 421,978 By Matching Biggest Common Factor Method
Now, list down the factors of 421
:1,421
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Greatest Common Factor
We found the factors 421,978 . The biggest common factor number is the GCF number.
So the greatest common factor 421,978 is 1.
Lets's calculate LCM of 535,705
| 5 | 535, 705 |
| 107, 141 |
∴ So the LCM of the given numbers is 5 x 107 x 141 = 75435
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/75435
Therefore, the GCF of Fractions 421/535,978/705 is 1/75435
Least Common Multiple of 535,705 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 535,705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(535,705) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(535,705) x common factors =5 x 1 = 5
LCM(535,705) = ( 535 × 705 ) / 5
LCM(535,705) = 377175 / 5
LCM(535,705) = 75435
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FAQs on GCF of Fractions of 421/535, 978/705
1. What is the HCF of 421,978?
The HCF of 421,978 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 421/535, 978/705?
Answer: GCF of Numerators as per given numbers 421/535, 978/705 is
GCF of Numerators i.e. for 421,978 is 1
LCM of denominators i.e. for 535,705 is 75435.
Thus, GCF of Fractions is 1/75435.Finally, GCF of Fractions for 421/535, 978/705 is 1/75435.