Use our free GCF of Fractions Calculator tool to compute the GCF of 749/138, 644/946 i.e 7/65274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/138, 644/946.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 749/138,644/946
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 749/138,644/946, numerators are 749,644
Denominators are 138,946
The GCF of 749,644 is 7 .
LCM of 138,946 is 65274.
The greatest common factor of 749/138,644/946 = [GCF of 749,644]/[LCM of 138,946]= 7/65274
Therefore, the GCF of 749/138,644/946 is 7/65274.
To find the highest common factor of 749,644, we have to find the factors of both numbers and list the highest common factor.
The factors of 749 are 1, 7, 107, 749
The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644
The HCF of 749,644 is 7.
Lets's calculate GCF of 749,644
7 | 749, 644 |
107, 92 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 644
:1,2,4,7,14,23,28,46,92,161,322,644
Greatest Common Factor
We found the factors 749,644 . The biggest common factor number is the GCF number.
So the greatest common factor 749,644 is 7.
Lets's calculate LCM of 138,946
2 | 138, 946 |
69, 473 |
∴ So the LCM of the given numbers is 2 x 69 x 473 = 65274
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/65274
Therefore, the GCF of Fractions 749/138,644/946 is 7/65274
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 138,946 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(138,946) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(138,946) x common factors =2 x 1 = 2
LCM(138,946) = ( 138 × 946 ) / 2
LCM(138,946) = 130548 / 2
LCM(138,946) = 65274
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 749,644?
The HCF of 749,644 is 7
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 749/138, 644/946?
Answer: GCF of Numerators as per given numbers 749/138, 644/946 is
GCF of Numerators i.e. for 749,644 is 7
LCM of denominators i.e. for 138,946 is 65274.
Thus, GCF of Fractions is 7/65274.Finally, GCF of Fractions for 749/138, 644/946 is 7/65274.