GCF of 103/88, 312/7314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 103/88, 312/7314 i.e 1/321816 easily. The following is the detailed procedure to determine the greatest common factor of fractions 103/88, 312/7314.
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 103/88,312/7314?
Given fractions are 103/88,312/7314
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 103/88,312/7314, numerators are 103,312
Denominators are 88,7314
The GCF of 103,312 is 1 .
LCM of 88,7314 is 321816.
The greatest common factor of 103/88,312/7314 = [GCF of 103,312]/[LCM of 88,7314]= 1/321816
Therefore, the GCF of 103/88,312/7314 is 1/321816.
To find the highest common factor of 103,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 103 are 1, 103
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 103,312 is 1.
Lets's calculate GCF of 103,312
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 103,312 By Matching Biggest Common Factor Method
Now, list down the factors of 103
:1,103
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 103,312 . The biggest common factor number is the GCF number.
So the greatest common factor 103,312 is 1.
Lets's calculate LCM of 88,7314
| 2 | 88, 7314 |
| 44, 3657 |
∴ So the LCM of the given numbers is 2 x 44 x 3657 = 321816
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/321816
Therefore, the GCF of Fractions 103/88,312/7314 is 1/321816
Least Common Multiple of 88,7314 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 88,7314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(88,7314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(88,7314) x common factors =2 x 1 = 2
LCM(88,7314) = ( 88 × 7314 ) / 2
LCM(88,7314) = 643632 / 2
LCM(88,7314) = 321816
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 103/88, 312/7314
1. What is the HCF of 103,312?
The HCF of 103,312 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 103/88, 312/7314?
Answer: GCF of Numerators as per given numbers 103/88, 312/7314 is
GCF of Numerators i.e. for 103,312 is 1
LCM of denominators i.e. for 88,7314 is 321816.
Thus, GCF of Fractions is 1/321816.Finally, GCF of Fractions for 103/88, 312/7314 is 1/321816.