Use our free GCF of Fractions Calculator tool to compute the GCF of 762/310, 688/635 i.e 2/39370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 762/310, 688/635.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 762/310,688/635
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 762/310,688/635, numerators are 762,688
Denominators are 310,635
The GCF of 762,688 is 2 .
LCM of 310,635 is 39370.
The greatest common factor of 762/310,688/635 = [GCF of 762,688]/[LCM of 310,635]= 2/39370
Therefore, the GCF of 762/310,688/635 is 2/39370.
To find the highest common factor of 762,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 762,688 is 2.
Lets's calculate GCF of 762,688
2 | 762, 688 |
381, 344 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 762,688 . The biggest common factor number is the GCF number.
So the greatest common factor 762,688 is 2.
Lets's calculate LCM of 310,635
5 | 310, 635 |
62, 127 |
∴ So the LCM of the given numbers is 5 x 62 x 127 = 39370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/39370
Therefore, the GCF of Fractions 762/310,688/635 is 2/39370
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 310,635 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(310,635) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(310,635) x common factors =5 x 1 = 5
LCM(310,635) = ( 310 × 635 ) / 5
LCM(310,635) = 196850 / 5
LCM(310,635) = 39370
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 762,688?
The HCF of 762,688 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 762/310, 688/635?
Answer: GCF of Numerators as per given numbers 762/310, 688/635 is
GCF of Numerators i.e. for 762,688 is 2
LCM of denominators i.e. for 310,635 is 39370.
Thus, GCF of Fractions is 2/39370.Finally, GCF of Fractions for 762/310, 688/635 is 2/39370.