GCF of 70/406, 60/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/406, 60/314 i.e 10/63742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/406, 60/314.
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 70/406,60/314?
Given fractions are 70/406,60/314
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 70/406,60/314, numerators are 70,60
Denominators are 406,314
The GCF of 70,60 is 10 .
LCM of 406,314 is 63742.
The greatest common factor of 70/406,60/314 = [GCF of 70,60]/[LCM of 406,314]= 10/63742
Therefore, the GCF of 70/406,60/314 is 10/63742.
To find the highest common factor of 70,60, 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 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The HCF of 70,60 is 10.
Lets's calculate GCF of 70,60
| 2 | 70, 60 |
| 5 | 35, 30 |
| 7, 6 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 70,60 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 60
:1,2,3,4,5,6,10,12,15,20,30,60
Greatest Common Factor
We found the factors 70,60 . The biggest common factor number is the GCF number.
So the greatest common factor 70,60 is 10.
Lets's calculate LCM of 406,314
| 2 | 406, 314 |
| 203, 157 |
∴ So the LCM of the given numbers is 2 x 203 x 157 = 63742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/63742
Therefore, the GCF of Fractions 70/406,60/314 is 10/63742
Least Common Multiple of 406,314 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 406,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,314) x common factors =2 x 1 = 2
LCM(406,314) = ( 406 × 314 ) / 2
LCM(406,314) = 127484 / 2
LCM(406,314) = 63742
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FAQs on GCF of Fractions of 70/406, 60/314
1. What is the HCF of 70,60?
The HCF of 70,60 is 10
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 70/406, 60/314?
Answer: GCF of Numerators as per given numbers 70/406, 60/314 is
GCF of Numerators i.e. for 70,60 is 10
LCM of denominators i.e. for 406,314 is 63742.
Thus, GCF of Fractions is 10/63742.Finally, GCF of Fractions for 70/406, 60/314 is 10/63742.