Use our free GCF of Fractions Calculator tool to compute the GCF of 8742/170, 6944/8156 i.e 62/693260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8742/170, 6944/8156.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8742/170,6944/8156
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 8742/170,6944/8156, numerators are 8742,6944
Denominators are 170,8156
The GCF of 8742,6944 is 62 .
LCM of 170,8156 is 693260.
The greatest common factor of 8742/170,6944/8156 = [GCF of 8742,6944]/[LCM of 170,8156]= 62/693260
Therefore, the GCF of 8742/170,6944/8156 is 62/693260.
To find the highest common factor of 8742,6944, we have to find the factors of both numbers and list the highest common factor.
The factors of 8742 are 1, 2, 3, 6, 31, 47, 62, 93, 94, 141, 186, 282, 1457, 2914, 4371, 8742
The factors of 6944 are 1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 112, 124, 217, 224, 248, 434, 496, 868, 992, 1736, 3472, 6944
The HCF of 8742,6944 is 62.
Lets's calculate GCF of 8742,6944
2 | 8742, 6944 |
31 | 4371, 3472 |
141, 112 |
∴ So the GCF of the given numbers is 2 x 31 = 62
Now, list down the factors of 8742
:1,2,3,6,31,47,62,93,94,141,186,282,1457,2914,4371,8742
Now, list down the factors of 6944
:1,2,4,7,8,14,16,28,31,32,56,62,112,124,217,224,248,434,496,868,992,1736,3472,6944
Greatest Common Factor
We found the factors 8742,6944 . The biggest common factor number is the GCF number.
So the greatest common factor 8742,6944 is 62.
Lets's calculate LCM of 170,8156
2 | 170, 8156 |
85, 4078 |
∴ So the LCM of the given numbers is 2 x 85 x 4078 = 693260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 62/693260
Therefore, the GCF of Fractions 8742/170,6944/8156 is 62/693260
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 170,8156 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(170,8156) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(170,8156) x common factors =2 x 1 = 2
LCM(170,8156) = ( 170 × 8156 ) / 2
LCM(170,8156) = 1386520 / 2
LCM(170,8156) = 693260
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 8742,6944?
The HCF of 8742,6944 is 62
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 8742/170, 6944/8156?
Answer: GCF of Numerators as per given numbers 8742/170, 6944/8156 is
GCF of Numerators i.e. for 8742,6944 is 62
LCM of denominators i.e. for 170,8156 is 693260.
Thus, GCF of Fractions is 62/693260.Finally, GCF of Fractions for 8742/170, 6944/8156 is 62/693260.