GCF of 210/42, 769/574
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 210/42, 769/574 i.e 1/1722 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/42, 769/574.
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 210/42,769/574?
Given fractions are 210/42,769/574
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 210/42,769/574, numerators are 210,769
Denominators are 42,574
The GCF of 210,769 is 1 .
LCM of 42,574 is 1722.
The greatest common factor of 210/42,769/574 = [GCF of 210,769]/[LCM of 42,574]= 1/1722
Therefore, the GCF of 210/42,769/574 is 1/1722.
To find the highest common factor of 210,769, 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 769 are 1, 769
The HCF of 210,769 is 1.
Lets's calculate GCF of 210,769
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 210,769 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 769
:1,769
Greatest Common Factor
We found the factors 210,769 . The biggest common factor number is the GCF number.
So the greatest common factor 210,769 is 1.
Lets's calculate LCM of 42,574
| 2 | 42, 574 |
| 7 | 21, 287 |
| 3, 41 |
∴ So the LCM of the given numbers is 2 x 7 x 3 x 41 = 1722
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1722
Therefore, the GCF of Fractions 210/42,769/574 is 1/1722
Least Common Multiple of 42,574 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 42,574 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,574) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(42,574) x common factors =14 x 1 = 14
LCM(42,574) = ( 42 × 574 ) / 14
LCM(42,574) = 24108 / 14
LCM(42,574) = 1722
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FAQs on GCF of Fractions of 210/42, 769/574
1. What is the HCF of 210,769?
The HCF of 210,769 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 210/42, 769/574?
Answer: GCF of Numerators as per given numbers 210/42, 769/574 is
GCF of Numerators i.e. for 210,769 is 1
LCM of denominators i.e. for 42,574 is 1722.
Thus, GCF of Fractions is 1/1722.Finally, GCF of Fractions for 210/42, 769/574 is 1/1722.