GCF of 704/70, 210/13, 240/69
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 704/70, 210/13, 240/69 i.e 2/62790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 704/70, 210/13, 240/69.
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 704/70,210/13,240/69?
Given fractions are 704/70,210/13,240/69
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 704/70,210/13,240/69, numerators are 704,210,240
Denominators are 70,13,69
The GCF of 704,210,240 is 2 .
LCM of 70,13,69 is 62790.
The greatest common factor of 704/70,210/13,240/69 = [GCF of 704,210,240]/[LCM of 70,13,69]= 2/62790
Therefore, the GCF of 704/70,210/13,240/69 is 2/62790.
To find the highest common factor of 704,210,240, we have to find the factors of both numbers and list the highest common factor.
The factors of 704 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
The HCF of 704,210,240 is 2.
Lets's calculate GCF of 704,210,240
| 2 | 704, 210, 240 |
| 352, 105, 120 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 704,210,240 By Matching Biggest Common Factor Method
Now, list down the factors of 704
:1,2,4,8,11,16,22,32,44,64,88,176,352,704
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 240
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240
Greatest Common Factor
We found the factors 704,210,240 . The biggest common factor number is the GCF number.
So the greatest common factor 704,210,240 is 2.
Lets's calculate LCM of 70,13,69
Given numbers has no common factors except 1. So, there LCM is their product i.e 62790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/62790
Therefore, the GCF of Fractions 704/70,210/13,240/69 is 2/62790
Least Common Multiple of 70,13,69 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 70,13,69 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,13,69) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(70,13,69) x common factors =1 x 1 = 1
LCM(70,13,69) = ( 70 × 13 × 69 ) / 1
LCM(70,13,69) = 62790 / 1
LCM(70,13,69) = 62790
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FAQs on GCF of Fractions of 704/70, 210/13, 240/69
1. What is the HCF of 704,210,240?
The HCF of 704,210,240 is 2
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 704/70, 210/13, 240/69?
Answer: GCF of Numerators as per given numbers 704/70, 210/13, 240/69 is
GCF of Numerators i.e. for 704,210,240 is 2
LCM of denominators i.e. for 70,13,69 is 62790.
Thus, GCF of Fractions is 2/62790.Finally, GCF of Fractions for 704/70, 210/13, 240/69 is 2/62790.