GCF of 693/312, 830/780
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 693/312, 830/780 i.e 1/1560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 693/312, 830/780.
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 693/312,830/780?
Given fractions are 693/312,830/780
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 693/312,830/780, numerators are 693,830
Denominators are 312,780
The GCF of 693,830 is 1 .
LCM of 312,780 is 1560.
The greatest common factor of 693/312,830/780 = [GCF of 693,830]/[LCM of 312,780]= 1/1560
Therefore, the GCF of 693/312,830/780 is 1/1560.
To find the highest common factor of 693,830, we have to find the factors of both numbers and list the highest common factor.
The factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The HCF of 693,830 is 1.
Lets's calculate GCF of 693,830
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 693,830 By Matching Biggest Common Factor Method
Now, list down the factors of 693
:1,3,7,9,11,21,33,63,77,99,231,693
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Greatest Common Factor
We found the factors 693,830 . The biggest common factor number is the GCF number.
So the greatest common factor 693,830 is 1.
Lets's calculate LCM of 312,780
| 2 | 312, 780 |
| 2 | 156, 390 |
| 3 | 78, 195 |
| 13 | 26, 65 |
| 2, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 2 x 5 = 1560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1560
Therefore, the GCF of Fractions 693/312,830/780 is 1/1560
Least Common Multiple of 312,780 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 312,780 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,780) = 156
common factors(in case of two or more numbers have common factors) = 1
GCF(312,780) x common factors =156 x 1 = 156
LCM(312,780) = ( 312 × 780 ) / 156
LCM(312,780) = 243360 / 156
LCM(312,780) = 1560
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FAQs on GCF of Fractions of 693/312, 830/780
1. What is the HCF of 693,830?
The HCF of 693,830 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 693/312, 830/780?
Answer: GCF of Numerators as per given numbers 693/312, 830/780 is
GCF of Numerators i.e. for 693,830 is 1
LCM of denominators i.e. for 312,780 is 1560.
Thus, GCF of Fractions is 1/1560.Finally, GCF of Fractions for 693/312, 830/780 is 1/1560.