Use our free GCF of Fractions Calculator tool to compute the GCF of 742/822, 780/752, 715/618 i.e 1/31834416 easily. The following is the detailed procedure to determine the greatest common factor of fractions 742/822, 780/752, 715/618.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 742/822,780/752,715/618
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 742/822,780/752,715/618, numerators are 742,780,715
Denominators are 822,752,618
The GCF of 742,780,715 is 1 .
LCM of 822,752,618 is 31834416.
The greatest common factor of 742/822,780/752,715/618 = [GCF of 742,780,715]/[LCM of 822,752,618]= 1/31834416
Therefore, the GCF of 742/822,780/752,715/618 is 1/31834416.
To find the highest common factor of 742,780,715, we have to find the factors of both numbers and list the highest common factor.
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The factors of 715 are 1, 5, 11, 13, 55, 65, 143, 715
The HCF of 742,780,715 is 1.
Lets's calculate GCF of 742,780,715
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Now, list down the factors of 715
:1,5,11,13,55,65,143,715
Greatest Common Factor
We found the factors 742,780,715 . The biggest common factor number is the GCF number.
So the greatest common factor 742,780,715 is 1.
Lets's calculate LCM of 822,752,618
2 | 822, 752, 618 |
3 | 411, 376, 309 |
137, 376, 103 |
∴ So the LCM of the given numbers is 2 x 3 x 137 x 376 x 103 = 31834416
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31834416
Therefore, the GCF of Fractions 742/822,780/752,715/618 is 1/31834416
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 822,752,618 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(822,752,618) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(822,752,618) x common factors =2 x 6 = 12
LCM(822,752,618) = ( 822 × 752 × 618 ) / 12
LCM(822,752,618) = 382012992 / 12
LCM(822,752,618) = 31834416
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 742,780,715?
The HCF of 742,780,715 is 1
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 742/822, 780/752, 715/618?
Answer: GCF of Numerators as per given numbers 742/822, 780/752, 715/618 is
GCF of Numerators i.e. for 742,780,715 is 1
LCM of denominators i.e. for 822,752,618 is 31834416.
Thus, GCF of Fractions is 1/31834416.Finally, GCF of Fractions for 742/822, 780/752, 715/618 is 1/31834416.