GCF of 649/678, 448/316
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 649/678, 448/316 i.e 1/107124 easily. The following is the detailed procedure to determine the greatest common factor of fractions 649/678, 448/316.
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 649/678,448/316?
Given fractions are 649/678,448/316
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 649/678,448/316, numerators are 649,448
Denominators are 678,316
The GCF of 649,448 is 1 .
LCM of 678,316 is 107124.
The greatest common factor of 649/678,448/316 = [GCF of 649,448]/[LCM of 678,316]= 1/107124
Therefore, the GCF of 649/678,448/316 is 1/107124.
To find the highest common factor of 649,448, we have to find the factors of both numbers and list the highest common factor.
The factors of 649 are 1, 11, 59, 649
The factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448
The HCF of 649,448 is 1.
Lets's calculate GCF of 649,448
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 649,448 By Matching Biggest Common Factor Method
Now, list down the factors of 649
:1,11,59,649
Now, list down the factors of 448
:1,2,4,7,8,14,16,28,32,56,64,112,224,448
Greatest Common Factor
We found the factors 649,448 . The biggest common factor number is the GCF number.
So the greatest common factor 649,448 is 1.
Lets's calculate LCM of 678,316
| 2 | 678, 316 |
| 339, 158 |
∴ So the LCM of the given numbers is 2 x 339 x 158 = 107124
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/107124
Therefore, the GCF of Fractions 649/678,448/316 is 1/107124
Least Common Multiple of 678,316 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 678,316 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,316) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,316) x common factors =2 x 1 = 2
LCM(678,316) = ( 678 × 316 ) / 2
LCM(678,316) = 214248 / 2
LCM(678,316) = 107124
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FAQs on GCF of Fractions of 649/678, 448/316
1. What is the HCF of 649,448?
The HCF of 649,448 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 649/678, 448/316?
Answer: GCF of Numerators as per given numbers 649/678, 448/316 is
GCF of Numerators i.e. for 649,448 is 1
LCM of denominators i.e. for 678,316 is 107124.
Thus, GCF of Fractions is 1/107124.Finally, GCF of Fractions for 649/678, 448/316 is 1/107124.