GCF of 70/34, 742/83, 308/328
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/34, 742/83, 308/328 i.e 14/462808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/34, 742/83, 308/328.
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 70/34,742/83,308/328?
Given fractions are 70/34,742/83,308/328
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 70/34,742/83,308/328, numerators are 70,742,308
Denominators are 34,83,328
The GCF of 70,742,308 is 14 .
LCM of 34,83,328 is 462808.
The greatest common factor of 70/34,742/83,308/328 = [GCF of 70,742,308]/[LCM of 34,83,328]= 14/462808
Therefore, the GCF of 70/34,742/83,308/328 is 14/462808.
To find the highest common factor of 70,742,308, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
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 70,742,308 is 14.
Lets's calculate GCF of 70,742,308
| 2 | 70, 742, 308 |
| 7 | 35, 371, 154 |
| 5, 53, 22 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 70,742,308 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
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 70,742,308 . The biggest common factor number is the GCF number.
So the greatest common factor 70,742,308 is 14.
Lets's calculate LCM of 34,83,328
| 2 | 34, 83, 328 |
| 17, 83, 164 |
∴ So the LCM of the given numbers is 2 x 17 x 83 x 164 = 462808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/462808
Therefore, the GCF of Fractions 70/34,742/83,308/328 is 14/462808
Least Common Multiple of 34,83,328 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 34,83,328 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(34,83,328) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(34,83,328) x common factors =1 x 2 = 2
LCM(34,83,328) = ( 34 × 83 × 328 ) / 2
LCM(34,83,328) = 925616 / 2
LCM(34,83,328) = 462808
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FAQs on GCF of Fractions of 70/34, 742/83, 308/328
1. What is the HCF of 70,742,308?
The HCF of 70,742,308 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 70/34, 742/83, 308/328?
Answer: GCF of Numerators as per given numbers 70/34, 742/83, 308/328 is
GCF of Numerators i.e. for 70,742,308 is 14
LCM of denominators i.e. for 34,83,328 is 462808.
Thus, GCF of Fractions is 14/462808.Finally, GCF of Fractions for 70/34, 742/83, 308/328 is 14/462808.