Use our free GCF of Fractions Calculator tool to compute the GCF of 832/774, 624/206 i.e 208/79722 easily. The following is the detailed procedure to determine the greatest common factor of fractions 832/774, 624/206.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 832/774,624/206
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 832/774,624/206, numerators are 832,624
Denominators are 774,206
The GCF of 832,624 is 208 .
LCM of 774,206 is 79722.
The greatest common factor of 832/774,624/206 = [GCF of 832,624]/[LCM of 774,206]= 208/79722
Therefore, the GCF of 832/774,624/206 is 208/79722.
To find the highest common factor of 832,624, we have to find the factors of both numbers and list the highest common factor.
The factors of 832 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832
The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
The HCF of 832,624 is 208.
Lets's calculate GCF of 832,624
2 | 832, 624 |
2 | 416, 312 |
2 | 208, 156 |
2 | 104, 78 |
13 | 52, 39 |
4, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 13 = 208
Now, list down the factors of 832
:1,2,4,8,13,16,26,32,52,64,104,208,416,832
Now, list down the factors of 624
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Greatest Common Factor
We found the factors 832,624 . The biggest common factor number is the GCF number.
So the greatest common factor 832,624 is 208.
Lets's calculate LCM of 774,206
2 | 774, 206 |
387, 103 |
∴ So the LCM of the given numbers is 2 x 387 x 103 = 79722
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 208/79722
Therefore, the GCF of Fractions 832/774,624/206 is 208/79722
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 774,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(774,206) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(774,206) x common factors =2 x 1 = 2
LCM(774,206) = ( 774 × 206 ) / 2
LCM(774,206) = 159444 / 2
LCM(774,206) = 79722
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 832,624?
The HCF of 832,624 is 208
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 832/774, 624/206?
Answer: GCF of Numerators as per given numbers 832/774, 624/206 is
GCF of Numerators i.e. for 832,624 is 208
LCM of denominators i.e. for 774,206 is 79722.
Thus, GCF of Fractions is 208/79722.Finally, GCF of Fractions for 832/774, 624/206 is 208/79722.