GCF of 738/722, 105/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 738/722, 105/196 i.e 3/70756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 738/722, 105/196.
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 738/722,105/196?
Given fractions are 738/722,105/196
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 738/722,105/196, numerators are 738,105
Denominators are 722,196
The GCF of 738,105 is 3 .
LCM of 722,196 is 70756.
The greatest common factor of 738/722,105/196 = [GCF of 738,105]/[LCM of 722,196]= 3/70756
Therefore, the GCF of 738/722,105/196 is 3/70756.
To find the highest common factor of 738,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 738,105 is 3.
Lets's calculate GCF of 738,105
| 3 | 738, 105 |
| 246, 35 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 738,105 By Matching Biggest Common Factor Method
Now, list down the factors of 738
:1,2,3,6,9,18,41,82,123,246,369,738
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 738,105 . The biggest common factor number is the GCF number.
So the greatest common factor 738,105 is 3.
Lets's calculate LCM of 722,196
| 2 | 722, 196 |
| 361, 98 |
∴ So the LCM of the given numbers is 2 x 361 x 98 = 70756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/70756
Therefore, the GCF of Fractions 738/722,105/196 is 3/70756
Least Common Multiple of 722,196 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 722,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(722,196) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(722,196) x common factors =2 x 1 = 2
LCM(722,196) = ( 722 × 196 ) / 2
LCM(722,196) = 141512 / 2
LCM(722,196) = 70756
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FAQs on GCF of Fractions of 738/722, 105/196
1. What is the HCF of 738,105?
The HCF of 738,105 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 738/722, 105/196?
Answer: GCF of Numerators as per given numbers 738/722, 105/196 is
GCF of Numerators i.e. for 738,105 is 3
LCM of denominators i.e. for 722,196 is 70756.
Thus, GCF of Fractions is 3/70756.Finally, GCF of Fractions for 738/722, 105/196 is 3/70756.