GCF of 210/751, 7470/825
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 210/751, 7470/825 i.e 30/619575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/751, 7470/825.
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 210/751,7470/825?
Given fractions are 210/751,7470/825
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 210/751,7470/825, numerators are 210,7470
Denominators are 751,825
The GCF of 210,7470 is 30 .
LCM of 751,825 is 619575.
The greatest common factor of 210/751,7470/825 = [GCF of 210,7470]/[LCM of 751,825]= 30/619575
Therefore, the GCF of 210/751,7470/825 is 30/619575.
To find the highest common factor of 210,7470, 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 7470 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 83, 90, 166, 249, 415, 498, 747, 830, 1245, 1494, 2490, 3735, 7470
The HCF of 210,7470 is 30.
Lets's calculate GCF of 210,7470
| 2 | 210, 7470 |
| 3 | 105, 3735 |
| 5 | 35, 1245 |
| 7, 249 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 210,7470 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 7470
:1,2,3,5,6,9,10,15,18,30,45,83,90,166,249,415,498,747,830,1245,1494,2490,3735,7470
Greatest Common Factor
We found the factors 210,7470 . The biggest common factor number is the GCF number.
So the greatest common factor 210,7470 is 30.
Lets's calculate LCM of 751,825
Given numbers has no common factors except 1. So, there LCM is their product i.e 619575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/619575
Therefore, the GCF of Fractions 210/751,7470/825 is 30/619575
Least Common Multiple of 751,825 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 751,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(751,825) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(751,825) x common factors =1 x 1 = 1
LCM(751,825) = ( 751 × 825 ) / 1
LCM(751,825) = 619575 / 1
LCM(751,825) = 619575
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FAQs on GCF of Fractions of 210/751, 7470/825
1. What is the HCF of 210,7470?
The HCF of 210,7470 is 30
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 210/751, 7470/825?
Answer: GCF of Numerators as per given numbers 210/751, 7470/825 is
GCF of Numerators i.e. for 210,7470 is 30
LCM of denominators i.e. for 751,825 is 619575.
Thus, GCF of Fractions is 30/619575.Finally, GCF of Fractions for 210/751, 7470/825 is 30/619575.