GCF of 328/977, 123/310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 328/977, 123/310 i.e 41/302870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 328/977, 123/310.
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 328/977,123/310?
Given fractions are 328/977,123/310
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 328/977,123/310, numerators are 328,123
Denominators are 977,310
The GCF of 328,123 is 41 .
LCM of 977,310 is 302870.
The greatest common factor of 328/977,123/310 = [GCF of 328,123]/[LCM of 977,310]= 41/302870
Therefore, the GCF of 328/977,123/310 is 41/302870.
To find the highest common factor of 328,123, we have to find the factors of both numbers and list the highest common factor.
The factors of 328 are 1, 2, 4, 8, 41, 82, 164, 328
The factors of 123 are 1, 3, 41, 123
The HCF of 328,123 is 41.
Lets's calculate GCF of 328,123
| 41 | 328, 123 |
| 8, 3 |
∴ So the GCF of the given numbers is 41 = 41
Greatest Common Factor of 328,123 By Matching Biggest Common Factor Method
Now, list down the factors of 328
:1,2,4,8,41,82,164,328
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 328,123 . The biggest common factor number is the GCF number.
So the greatest common factor 328,123 is 41.
Lets's calculate LCM of 977,310
Given numbers has no common factors except 1. So, there LCM is their product i.e 302870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/302870
Therefore, the GCF of Fractions 328/977,123/310 is 41/302870
Least Common Multiple of 977,310 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 977,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(977,310) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(977,310) x common factors =1 x 1 = 1
LCM(977,310) = ( 977 × 310 ) / 1
LCM(977,310) = 302870 / 1
LCM(977,310) = 302870
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FAQs on GCF of Fractions of 328/977, 123/310
1. What is the HCF of 328,123?
The HCF of 328,123 is 41
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 328/977, 123/310?
Answer: GCF of Numerators as per given numbers 328/977, 123/310 is
GCF of Numerators i.e. for 328,123 is 41
LCM of denominators i.e. for 977,310 is 302870.
Thus, GCF of Fractions is 41/302870.Finally, GCF of Fractions for 328/977, 123/310 is 41/302870.