GCF of 830/693, 1400/189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 830/693, 1400/189 i.e 10/2079 easily. The following is the detailed procedure to determine the greatest common factor of fractions 830/693, 1400/189.
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 830/693,1400/189?
Given fractions are 830/693,1400/189
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 830/693,1400/189, numerators are 830,1400
Denominators are 693,189
The GCF of 830,1400 is 10 .
LCM of 693,189 is 2079.
The greatest common factor of 830/693,1400/189 = [GCF of 830,1400]/[LCM of 693,189]= 10/2079
Therefore, the GCF of 830/693,1400/189 is 10/2079.
To find the highest common factor of 830,1400, we have to find the factors of both numbers and list the highest common factor.
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400
The HCF of 830,1400 is 10.
Lets's calculate GCF of 830,1400
| 2 | 830, 1400 |
| 5 | 415, 700 |
| 83, 140 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 830,1400 By Matching Biggest Common Factor Method
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Now, list down the factors of 1400
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,140,175,200,280,350,700,1400
Greatest Common Factor
We found the factors 830,1400 . The biggest common factor number is the GCF number.
So the greatest common factor 830,1400 is 10.
Lets's calculate LCM of 693,189
| 3 | 693, 189 |
| 3 | 231, 63 |
| 7 | 77, 21 |
| 11, 3 |
∴ So the LCM of the given numbers is 3 x 3 x 7 x 11 x 3 = 2079
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/2079
Therefore, the GCF of Fractions 830/693,1400/189 is 10/2079
Least Common Multiple of 693,189 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 693,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(693,189) = 63
common factors(in case of two or more numbers have common factors) = 1
GCF(693,189) x common factors =63 x 1 = 63
LCM(693,189) = ( 693 × 189 ) / 63
LCM(693,189) = 130977 / 63
LCM(693,189) = 2079
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FAQs on GCF of Fractions of 830/693, 1400/189
1. What is the HCF of 830,1400?
The HCF of 830,1400 is 10
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 830/693, 1400/189?
Answer: GCF of Numerators as per given numbers 830/693, 1400/189 is
GCF of Numerators i.e. for 830,1400 is 10
LCM of denominators i.e. for 693,189 is 2079.
Thus, GCF of Fractions is 10/2079.Finally, GCF of Fractions for 830/693, 1400/189 is 10/2079.