GCF of 40/70, 210/42, 185/614
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/70, 210/42, 185/614 i.e 5/64470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/70, 210/42, 185/614.
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 40/70,210/42,185/614?
Given fractions are 40/70,210/42,185/614
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 40/70,210/42,185/614, numerators are 40,210,185
Denominators are 70,42,614
The GCF of 40,210,185 is 5 .
LCM of 70,42,614 is 64470.
The greatest common factor of 40/70,210/42,185/614 = [GCF of 40,210,185]/[LCM of 70,42,614]= 5/64470
Therefore, the GCF of 40/70,210/42,185/614 is 5/64470.
To find the highest common factor of 40,210,185, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 185 are 1, 5, 37, 185
The HCF of 40,210,185 is 5.
Lets's calculate GCF of 40,210,185
| 5 | 40, 210, 185 |
| 8, 42, 37 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 40,210,185 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Now, list down the factors of 185
:1,5,37,185
Greatest Common Factor
We found the factors 40,210,185 . The biggest common factor number is the GCF number.
So the greatest common factor 40,210,185 is 5.
Lets's calculate LCM of 70,42,614
| 2 | 70, 42, 614 |
| 7 | 35, 21, 307 |
| 5, 3, 307 |
∴ So the LCM of the given numbers is 2 x 7 x 5 x 3 x 307 = 64470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/64470
Therefore, the GCF of Fractions 40/70,210/42,185/614 is 5/64470
Least Common Multiple of 70,42,614 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 70,42,614 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,42,614) = 2
common factors(in case of two or more numbers have common factors) = 14
GCF(70,42,614) x common factors =2 x 14 = 28
LCM(70,42,614) = ( 70 × 42 × 614 ) / 28
LCM(70,42,614) = 1805160 / 28
LCM(70,42,614) = 64470
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FAQs on GCF of Fractions of 40/70, 210/42, 185/614
1. What is the HCF of 40,210,185?
The HCF of 40,210,185 is 5
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 40/70, 210/42, 185/614?
Answer: GCF of Numerators as per given numbers 40/70, 210/42, 185/614 is
GCF of Numerators i.e. for 40,210,185 is 5
LCM of denominators i.e. for 70,42,614 is 64470.
Thus, GCF of Fractions is 5/64470.Finally, GCF of Fractions for 40/70, 210/42, 185/614 is 5/64470.