GCF of 98/406, 742/470, 308/363
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 98/406, 742/470, 308/363 i.e 14/34633830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 98/406, 742/470, 308/363.
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 98/406,742/470,308/363?
Given fractions are 98/406,742/470,308/363
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 98/406,742/470,308/363, numerators are 98,742,308
Denominators are 406,470,363
The GCF of 98,742,308 is 14 .
LCM of 406,470,363 is 34633830.
The greatest common factor of 98/406,742/470,308/363 = [GCF of 98,742,308]/[LCM of 406,470,363]= 14/34633830
Therefore, the GCF of 98/406,742/470,308/363 is 14/34633830.
To find the highest common factor of 98,742,308, we have to find the factors of both numbers and list the highest common factor.
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The HCF of 98,742,308 is 14.
Lets's calculate GCF of 98,742,308
| 2 | 98, 742, 308 |
| 7 | 49, 371, 154 |
| 7, 53, 22 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 98,742,308 By Matching Biggest Common Factor Method
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Greatest Common Factor
We found the factors 98,742,308 . The biggest common factor number is the GCF number.
So the greatest common factor 98,742,308 is 14.
Lets's calculate LCM of 406,470,363
| 2 | 406, 470, 363 |
| 203, 235, 363 |
∴ So the LCM of the given numbers is 2 x 203 x 235 x 363 = 34633830
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/34633830
Therefore, the GCF of Fractions 98/406,742/470,308/363 is 14/34633830
Least Common Multiple of 406,470,363 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 406,470,363 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,470,363) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(406,470,363) x common factors =1 x 2 = 2
LCM(406,470,363) = ( 406 × 470 × 363 ) / 2
LCM(406,470,363) = 69267660 / 2
LCM(406,470,363) = 34633830
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FAQs on GCF of Fractions of 98/406, 742/470, 308/363
1. What is the HCF of 98,742,308?
The HCF of 98,742,308 is 14
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 98/406, 742/470, 308/363?
Answer: GCF of Numerators as per given numbers 98/406, 742/470, 308/363 is
GCF of Numerators i.e. for 98,742,308 is 14
LCM of denominators i.e. for 406,470,363 is 34633830.
Thus, GCF of Fractions is 14/34633830.Finally, GCF of Fractions for 98/406, 742/470, 308/363 is 14/34633830.