GCF of 978/70, 507/2154
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 978/70, 507/2154 i.e 3/75390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 978/70, 507/2154.
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 978/70,507/2154?
Given fractions are 978/70,507/2154
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 978/70,507/2154, numerators are 978,507
Denominators are 70,2154
The GCF of 978,507 is 3 .
LCM of 70,2154 is 75390.
The greatest common factor of 978/70,507/2154 = [GCF of 978,507]/[LCM of 70,2154]= 3/75390
Therefore, the GCF of 978/70,507/2154 is 3/75390.
To find the highest common factor of 978,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 978,507 is 3.
Lets's calculate GCF of 978,507
| 3 | 978, 507 |
| 326, 169 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 978,507 By Matching Biggest Common Factor Method
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 978,507 . The biggest common factor number is the GCF number.
So the greatest common factor 978,507 is 3.
Lets's calculate LCM of 70,2154
| 2 | 70, 2154 |
| 35, 1077 |
∴ So the LCM of the given numbers is 2 x 35 x 1077 = 75390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/75390
Therefore, the GCF of Fractions 978/70,507/2154 is 3/75390
Least Common Multiple of 70,2154 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 70,2154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,2154) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(70,2154) x common factors =2 x 1 = 2
LCM(70,2154) = ( 70 × 2154 ) / 2
LCM(70,2154) = 150780 / 2
LCM(70,2154) = 75390
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FAQs on GCF of Fractions of 978/70, 507/2154
1. What is the HCF of 978,507?
The HCF of 978,507 is 3
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 978/70, 507/2154?
Answer: GCF of Numerators as per given numbers 978/70, 507/2154 is
GCF of Numerators i.e. for 978,507 is 3
LCM of denominators i.e. for 70,2154 is 75390.
Thus, GCF of Fractions is 3/75390.Finally, GCF of Fractions for 978/70, 507/2154 is 3/75390.