GCF of 663/680, 312/694
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 663/680, 312/694 i.e 39/235960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 663/680, 312/694.
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 663/680,312/694?
Given fractions are 663/680,312/694
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 663/680,312/694, numerators are 663,312
Denominators are 680,694
The GCF of 663,312 is 39 .
LCM of 680,694 is 235960.
The greatest common factor of 663/680,312/694 = [GCF of 663,312]/[LCM of 680,694]= 39/235960
Therefore, the GCF of 663/680,312/694 is 39/235960.
To find the highest common factor of 663,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 663,312 is 39.
Lets's calculate GCF of 663,312
| 3 | 663, 312 |
| 13 | 221, 104 |
| 17, 8 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Greatest Common Factor of 663,312 By Matching Biggest Common Factor Method
Now, list down the factors of 663
:1,3,13,17,39,51,221,663
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 663,312 . The biggest common factor number is the GCF number.
So the greatest common factor 663,312 is 39.
Lets's calculate LCM of 680,694
| 2 | 680, 694 |
| 340, 347 |
∴ So the LCM of the given numbers is 2 x 340 x 347 = 235960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/235960
Therefore, the GCF of Fractions 663/680,312/694 is 39/235960
Least Common Multiple of 680,694 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 680,694 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,694) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(680,694) x common factors =2 x 1 = 2
LCM(680,694) = ( 680 × 694 ) / 2
LCM(680,694) = 471920 / 2
LCM(680,694) = 235960
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FAQs on GCF of Fractions of 663/680, 312/694
1. What is the HCF of 663,312?
The HCF of 663,312 is 39
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 663/680, 312/694?
Answer: GCF of Numerators as per given numbers 663/680, 312/694 is
GCF of Numerators i.e. for 663,312 is 39
LCM of denominators i.e. for 680,694 is 235960.
Thus, GCF of Fractions is 39/235960.Finally, GCF of Fractions for 663/680, 312/694 is 39/235960.