GCF of 58/220, 78/500, 278/498
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 58/220, 78/500, 278/498 i.e 2/1369500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 58/220, 78/500, 278/498.
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 58/220,78/500,278/498?
Given fractions are 58/220,78/500,278/498
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 58/220,78/500,278/498, numerators are 58,78,278
Denominators are 220,500,498
The GCF of 58,78,278 is 2 .
LCM of 220,500,498 is 1369500.
The greatest common factor of 58/220,78/500,278/498 = [GCF of 58,78,278]/[LCM of 220,500,498]= 2/1369500
Therefore, the GCF of 58/220,78/500,278/498 is 2/1369500.
To find the highest common factor of 58,78,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 58 are 1, 2, 29, 58
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 278 are 1, 2, 139, 278
The HCF of 58,78,278 is 2.
Lets's calculate GCF of 58,78,278
| 2 | 58, 78, 278 |
| 29, 39, 139 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 58,78,278 By Matching Biggest Common Factor Method
Now, list down the factors of 58
:1,2,29,58
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 58,78,278 . The biggest common factor number is the GCF number.
So the greatest common factor 58,78,278 is 2.
Lets's calculate LCM of 220,500,498
| 2 | 220, 500, 498 |
| 2 | 110, 250, 249 |
| 5 | 55, 125, 249 |
| 11, 25, 249 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 11 x 25 x 249 = 1369500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1369500
Therefore, the GCF of Fractions 58/220,78/500,278/498 is 2/1369500
Least Common Multiple of 220,500,498 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 220,500,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(220,500,498) = 2
common factors(in case of two or more numbers have common factors) = 20
GCF(220,500,498) x common factors =2 x 20 = 40
LCM(220,500,498) = ( 220 × 500 × 498 ) / 40
LCM(220,500,498) = 54780000 / 40
LCM(220,500,498) = 1369500
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FAQs on GCF of Fractions of 58/220, 78/500, 278/498
1. What is the HCF of 58,78,278?
The HCF of 58,78,278 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 58/220, 78/500, 278/498?
Answer: GCF of Numerators as per given numbers 58/220, 78/500, 278/498 is
GCF of Numerators i.e. for 58,78,278 is 2
LCM of denominators i.e. for 220,500,498 is 1369500.
Thus, GCF of Fractions is 2/1369500.Finally, GCF of Fractions for 58/220, 78/500, 278/498 is 2/1369500.