GCF of 878/60, 402/48, 560/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 878/60, 402/48, 560/31 i.e 2/7440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 878/60, 402/48, 560/31.
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 878/60,402/48,560/31?
Given fractions are 878/60,402/48,560/31
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 878/60,402/48,560/31, numerators are 878,402,560
Denominators are 60,48,31
The GCF of 878,402,560 is 2 .
LCM of 60,48,31 is 7440.
The greatest common factor of 878/60,402/48,560/31 = [GCF of 878,402,560]/[LCM of 60,48,31]= 2/7440
Therefore, the GCF of 878/60,402/48,560/31 is 2/7440.
To find the highest common factor of 878,402,560, we have to find the factors of both numbers and list the highest common factor.
The factors of 878 are 1, 2, 439, 878
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 878,402,560 is 2.
Lets's calculate GCF of 878,402,560
| 2 | 878, 402, 560 |
| 439, 201, 280 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 878,402,560 By Matching Biggest Common Factor Method
Now, list down the factors of 878
:1,2,439,878
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 878,402,560 . The biggest common factor number is the GCF number.
So the greatest common factor 878,402,560 is 2.
Lets's calculate LCM of 60,48,31
| 2 | 60, 48, 31 |
| 2 | 30, 24, 31 |
| 3 | 15, 12, 31 |
| 5, 4, 31 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 4 x 31 = 7440
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7440
Therefore, the GCF of Fractions 878/60,402/48,560/31 is 2/7440
Least Common Multiple of 60,48,31 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 60,48,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,48,31) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(60,48,31) x common factors =1 x 12 = 12
LCM(60,48,31) = ( 60 × 48 × 31 ) / 12
LCM(60,48,31) = 89280 / 12
LCM(60,48,31) = 7440
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FAQs on GCF of Fractions of 878/60, 402/48, 560/31
1. What is the HCF of 878,402,560?
The HCF of 878,402,560 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 878/60, 402/48, 560/31?
Answer: GCF of Numerators as per given numbers 878/60, 402/48, 560/31 is
GCF of Numerators i.e. for 878,402,560 is 2
LCM of denominators i.e. for 60,48,31 is 7440.
Thus, GCF of Fractions is 2/7440.Finally, GCF of Fractions for 878/60, 402/48, 560/31 is 2/7440.