GCF of 736/10, 870/69, 538/23
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 736/10, 870/69, 538/23 i.e 2/690 easily. The following is the detailed procedure to determine the greatest common factor of fractions 736/10, 870/69, 538/23.
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 736/10,870/69,538/23?
Given fractions are 736/10,870/69,538/23
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 736/10,870/69,538/23, numerators are 736,870,538
Denominators are 10,69,23
The GCF of 736,870,538 is 2 .
LCM of 10,69,23 is 690.
The greatest common factor of 736/10,870/69,538/23 = [GCF of 736,870,538]/[LCM of 10,69,23]= 2/690
Therefore, the GCF of 736/10,870/69,538/23 is 2/690.
To find the highest common factor of 736,870,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The factors of 538 are 1, 2, 269, 538
The HCF of 736,870,538 is 2.
Lets's calculate GCF of 736,870,538
| 2 | 736, 870, 538 |
| 368, 435, 269 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 736,870,538 By Matching Biggest Common Factor Method
Now, list down the factors of 736
:1,2,4,8,16,23,32,46,92,184,368,736
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 736,870,538 . The biggest common factor number is the GCF number.
So the greatest common factor 736,870,538 is 2.
Lets's calculate LCM of 10,69,23
| 23 | 10, 69, 23 |
| 10, 3, 1 |
∴ So the LCM of the given numbers is 23 x 10 x 3 x 1 = 690
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/690
Therefore, the GCF of Fractions 736/10,870/69,538/23 is 2/690
Least Common Multiple of 10,69,23 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 10,69,23 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,69,23) = 1
common factors(in case of two or more numbers have common factors) = 23
GCF(10,69,23) x common factors =1 x 23 = 23
LCM(10,69,23) = ( 10 × 69 × 23 ) / 23
LCM(10,69,23) = 15870 / 23
LCM(10,69,23) = 690
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FAQs on GCF of Fractions of 736/10, 870/69, 538/23
1. What is the HCF of 736,870,538?
The HCF of 736,870,538 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 736/10, 870/69, 538/23?
Answer: GCF of Numerators as per given numbers 736/10, 870/69, 538/23 is
GCF of Numerators i.e. for 736,870,538 is 2
LCM of denominators i.e. for 10,69,23 is 690.
Thus, GCF of Fractions is 2/690.Finally, GCF of Fractions for 736/10, 870/69, 538/23 is 2/690.