GCF of 316/53, 119/78, 870/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 316/53, 119/78, 870/78 i.e 1/4134 easily. The following is the detailed procedure to determine the greatest common factor of fractions 316/53, 119/78, 870/78.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 316/53,119/78,870/78?
Given fractions are 316/53,119/78,870/78
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 316/53,119/78,870/78, numerators are 316,119,870
Denominators are 53,78,78
The GCF of 316,119,870 is 1 .
LCM of 53,78,78 is 4134.
The greatest common factor of 316/53,119/78,870/78 = [GCF of 316,119,870]/[LCM of 53,78,78]= 1/4134
Therefore, the GCF of 316/53,119/78,870/78 is 1/4134.
To find the highest common factor of 316,119,870, we have to find the factors of both numbers and list the highest common factor.
The factors of 316 are 1, 2, 4, 79, 158, 316
The factors of 119 are 1, 7, 17, 119
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The HCF of 316,119,870 is 1.
Lets's calculate GCF of 316,119,870
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 316,119,870 By Matching Biggest Common Factor Method
Now, list down the factors of 316
:1,2,4,79,158,316
Now, list down the factors of 119
:1,7,17,119
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Greatest Common Factor
We found the factors 316,119,870 . The biggest common factor number is the GCF number.
So the greatest common factor 316,119,870 is 1.
Lets's calculate LCM of 53,78,78
| 2 | 53, 78, 78 |
| 3 | 53, 39, 39 |
| 13 | 53, 13, 13 |
| 53, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 53 x 1 x 1 = 4134
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4134
Therefore, the GCF of Fractions 316/53,119/78,870/78 is 1/4134
Least Common Multiple of 53,78,78 with GCF Formula
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 53,78,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,78,78) = 1
common factors(in case of two or more numbers have common factors) = 78
GCF(53,78,78) x common factors =1 x 78 = 78
LCM(53,78,78) = ( 53 × 78 × 78 ) / 78
LCM(53,78,78) = 322452 / 78
LCM(53,78,78) = 4134
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FAQs on GCF of Fractions of 316/53, 119/78, 870/78
1. What is the HCF of 316,119,870?
The HCF of 316,119,870 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 316/53, 119/78, 870/78?
Answer: GCF of Numerators as per given numbers 316/53, 119/78, 870/78 is
GCF of Numerators i.e. for 316,119,870 is 1
LCM of denominators i.e. for 53,78,78 is 4134.
Thus, GCF of Fractions is 1/4134.Finally, GCF of Fractions for 316/53, 119/78, 870/78 is 1/4134.