GCF of 89/42, 210/78, 406/356
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 89/42, 210/78, 406/356 i.e 1/97188 easily. The following is the detailed procedure to determine the greatest common factor of fractions 89/42, 210/78, 406/356.
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 89/42,210/78,406/356?
Given fractions are 89/42,210/78,406/356
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 89/42,210/78,406/356, numerators are 89,210,406
Denominators are 42,78,356
The GCF of 89,210,406 is 1 .
LCM of 42,78,356 is 97188.
The greatest common factor of 89/42,210/78,406/356 = [GCF of 89,210,406]/[LCM of 42,78,356]= 1/97188
Therefore, the GCF of 89/42,210/78,406/356 is 1/97188.
To find the highest common factor of 89,210,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 89 are 1, 89
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 89,210,406 is 1.
Lets's calculate GCF of 89,210,406
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 89,210,406 By Matching Biggest Common Factor Method
Now, list down the factors of 89
:1,89
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 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 89,210,406 . The biggest common factor number is the GCF number.
So the greatest common factor 89,210,406 is 1.
Lets's calculate LCM of 42,78,356
| 2 | 42, 78, 356 |
| 3 | 21, 39, 178 |
| 7, 13, 178 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 13 x 178 = 97188
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/97188
Therefore, the GCF of Fractions 89/42,210/78,406/356 is 1/97188
Least Common Multiple of 42,78,356 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 42,78,356 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,78,356) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(42,78,356) x common factors =2 x 6 = 12
LCM(42,78,356) = ( 42 × 78 × 356 ) / 12
LCM(42,78,356) = 1166256 / 12
LCM(42,78,356) = 97188
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FAQs on GCF of Fractions of 89/42, 210/78, 406/356
1. What is the HCF of 89,210,406?
The HCF of 89,210,406 is 1
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 89/42, 210/78, 406/356?
Answer: GCF of Numerators as per given numbers 89/42, 210/78, 406/356 is
GCF of Numerators i.e. for 89,210,406 is 1
LCM of denominators i.e. for 42,78,356 is 97188.
Thus, GCF of Fractions is 1/97188.Finally, GCF of Fractions for 89/42, 210/78, 406/356 is 1/97188.