GCF of 174/49, 978/805
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 174/49, 978/805 i.e 6/5635 easily. The following is the detailed procedure to determine the greatest common factor of fractions 174/49, 978/805.
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 174/49,978/805?
Given fractions are 174/49,978/805
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 174/49,978/805, numerators are 174,978
Denominators are 49,805
The GCF of 174,978 is 6 .
LCM of 49,805 is 5635.
The greatest common factor of 174/49,978/805 = [GCF of 174,978]/[LCM of 49,805]= 6/5635
Therefore, the GCF of 174/49,978/805 is 6/5635.
To find the highest common factor of 174,978, we have to find the factors of both numbers and list the highest common factor.
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The HCF of 174,978 is 6.
Lets's calculate GCF of 174,978
| 2 | 174, 978 |
| 3 | 87, 489 |
| 29, 163 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 174,978 By Matching Biggest Common Factor Method
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Greatest Common Factor
We found the factors 174,978 . The biggest common factor number is the GCF number.
So the greatest common factor 174,978 is 6.
Lets's calculate LCM of 49,805
| 7 | 49, 805 |
| 7, 115 |
∴ So the LCM of the given numbers is 7 x 7 x 115 = 5635
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/5635
Therefore, the GCF of Fractions 174/49,978/805 is 6/5635
Least Common Multiple of 49,805 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 49,805 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,805) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(49,805) x common factors =7 x 1 = 7
LCM(49,805) = ( 49 × 805 ) / 7
LCM(49,805) = 39445 / 7
LCM(49,805) = 5635
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FAQs on GCF of Fractions of 174/49, 978/805
1. What is the HCF of 174,978?
The HCF of 174,978 is 6
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 174/49, 978/805?
Answer: GCF of Numerators as per given numbers 174/49, 978/805 is
GCF of Numerators i.e. for 174,978 is 6
LCM of denominators i.e. for 49,805 is 5635.
Thus, GCF of Fractions is 6/5635.Finally, GCF of Fractions for 174/49, 978/805 is 6/5635.