GCF of 1314/457, 7419/914
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1314/457, 7419/914 i.e 3/914 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1314/457, 7419/914.
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 1314/457,7419/914?
Given fractions are 1314/457,7419/914
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 1314/457,7419/914, numerators are 1314,7419
Denominators are 457,914
The GCF of 1314,7419 is 3 .
LCM of 457,914 is 914.
The greatest common factor of 1314/457,7419/914 = [GCF of 1314,7419]/[LCM of 457,914]= 3/914
Therefore, the GCF of 1314/457,7419/914 is 3/914.
To find the highest common factor of 1314,7419, we have to find the factors of both numbers and list the highest common factor.
The factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314
The factors of 7419 are 1, 3, 2473, 7419
The HCF of 1314,7419 is 3.
Lets's calculate GCF of 1314,7419
| 3 | 1314, 7419 |
| 438, 2473 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 1314,7419 By Matching Biggest Common Factor Method
Now, list down the factors of 1314
:1,2,3,6,9,18,73,146,219,438,657,1314
Now, list down the factors of 7419
:1,3,2473,7419
Greatest Common Factor
We found the factors 1314,7419 . The biggest common factor number is the GCF number.
So the greatest common factor 1314,7419 is 3.
Lets's calculate LCM of 457,914
| 457 | 457, 914 |
| 1, 2 |
∴ So the LCM of the given numbers is 457 x 1 x 2 = 914
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/914
Therefore, the GCF of Fractions 1314/457,7419/914 is 3/914
Least Common Multiple of 457,914 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 457,914 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(457,914) = 457
common factors(in case of two or more numbers have common factors) = 1
GCF(457,914) x common factors =457 x 1 = 457
LCM(457,914) = ( 457 × 914 ) / 457
LCM(457,914) = 417698 / 457
LCM(457,914) = 914
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1314/457, 7419/914
1. What is the HCF of 1314,7419?
The HCF of 1314,7419 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 1314/457, 7419/914?
Answer: GCF of Numerators as per given numbers 1314/457, 7419/914 is
GCF of Numerators i.e. for 1314,7419 is 3
LCM of denominators i.e. for 457,914 is 914.
Thus, GCF of Fractions is 3/914.Finally, GCF of Fractions for 1314/457, 7419/914 is 3/914.