GCF of 210/15, 714/5768
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 210/15, 714/5768 i.e 42/86520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/15, 714/5768.
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 210/15,714/5768?
Given fractions are 210/15,714/5768
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 210/15,714/5768, numerators are 210,714
Denominators are 15,5768
The GCF of 210,714 is 42 .
LCM of 15,5768 is 86520.
The greatest common factor of 210/15,714/5768 = [GCF of 210,714]/[LCM of 15,5768]= 42/86520
Therefore, the GCF of 210/15,714/5768 is 42/86520.
To find the highest common factor of 210,714, we have to find the factors of both numbers and list the highest common factor.
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714
The HCF of 210,714 is 42.
Lets's calculate GCF of 210,714
| 2 | 210, 714 |
| 3 | 105, 357 |
| 7 | 35, 119 |
| 5, 17 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 210,714 By Matching Biggest Common Factor Method
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 714
:1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 210,714 . The biggest common factor number is the GCF number.
So the greatest common factor 210,714 is 42.
Lets's calculate LCM of 15,5768
Given numbers has no common factors except 1. So, there LCM is their product i.e 86520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/86520
Therefore, the GCF of Fractions 210/15,714/5768 is 42/86520
Least Common Multiple of 15,5768 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 15,5768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,5768) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(15,5768) x common factors =1 x 1 = 1
LCM(15,5768) = ( 15 × 5768 ) / 1
LCM(15,5768) = 86520 / 1
LCM(15,5768) = 86520
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FAQs on GCF of Fractions of 210/15, 714/5768
1. What is the HCF of 210,714?
The HCF of 210,714 is 42
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 210/15, 714/5768?
Answer: GCF of Numerators as per given numbers 210/15, 714/5768 is
GCF of Numerators i.e. for 210,714 is 42
LCM of denominators i.e. for 15,5768 is 86520.
Thus, GCF of Fractions is 42/86520.Finally, GCF of Fractions for 210/15, 714/5768 is 42/86520.