GCF of 3038/564, 3100/585
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3038/564, 3100/585 i.e 62/109980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3038/564, 3100/585.
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 3038/564,3100/585?
Given fractions are 3038/564,3100/585
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 3038/564,3100/585, numerators are 3038,3100
Denominators are 564,585
The GCF of 3038,3100 is 62 .
LCM of 564,585 is 109980.
The greatest common factor of 3038/564,3100/585 = [GCF of 3038,3100]/[LCM of 564,585]= 62/109980
Therefore, the GCF of 3038/564,3100/585 is 62/109980.
To find the highest common factor of 3038,3100, we have to find the factors of both numbers and list the highest common factor.
The factors of 3038 are 1, 2, 7, 14, 31, 49, 62, 98, 217, 434, 1519, 3038
The factors of 3100 are 1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 310, 620, 775, 1550, 3100
The HCF of 3038,3100 is 62.
Lets's calculate GCF of 3038,3100
| 2 | 3038, 3100 |
| 31 | 1519, 1550 |
| 49, 50 |
∴ So the GCF of the given numbers is 2 x 31 = 62
Greatest Common Factor of 3038,3100 By Matching Biggest Common Factor Method
Now, list down the factors of 3038
:1,2,7,14,31,49,62,98,217,434,1519,3038
Now, list down the factors of 3100
:1,2,4,5,10,20,25,31,50,62,100,124,155,310,620,775,1550,3100
Greatest Common Factor
We found the factors 3038,3100 . The biggest common factor number is the GCF number.
So the greatest common factor 3038,3100 is 62.
Lets's calculate LCM of 564,585
| 3 | 564, 585 |
| 188, 195 |
∴ So the LCM of the given numbers is 3 x 188 x 195 = 109980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 62/109980
Therefore, the GCF of Fractions 3038/564,3100/585 is 62/109980
Least Common Multiple of 564,585 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 564,585 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,585) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(564,585) x common factors =3 x 1 = 3
LCM(564,585) = ( 564 × 585 ) / 3
LCM(564,585) = 329940 / 3
LCM(564,585) = 109980
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FAQs on GCF of Fractions of 3038/564, 3100/585
1. What is the HCF of 3038,3100?
The HCF of 3038,3100 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 3038/564, 3100/585?
Answer: GCF of Numerators as per given numbers 3038/564, 3100/585 is
GCF of Numerators i.e. for 3038,3100 is 62
LCM of denominators i.e. for 564,585 is 109980.
Thus, GCF of Fractions is 62/109980.Finally, GCF of Fractions for 3038/564, 3100/585 is 62/109980.