GCF of 584/31, 506/30, 688/28
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 584/31, 506/30, 688/28 i.e 2/13020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 584/31, 506/30, 688/28.
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 584/31,506/30,688/28?
Given fractions are 584/31,506/30,688/28
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 584/31,506/30,688/28, numerators are 584,506,688
Denominators are 31,30,28
The GCF of 584,506,688 is 2 .
LCM of 31,30,28 is 13020.
The greatest common factor of 584/31,506/30,688/28 = [GCF of 584,506,688]/[LCM of 31,30,28]= 2/13020
Therefore, the GCF of 584/31,506/30,688/28 is 2/13020.
To find the highest common factor of 584,506,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 584,506,688 is 2.
Lets's calculate GCF of 584,506,688
| 2 | 584, 506, 688 |
| 292, 253, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 584,506,688 By Matching Biggest Common Factor Method
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 584,506,688 . The biggest common factor number is the GCF number.
So the greatest common factor 584,506,688 is 2.
Lets's calculate LCM of 31,30,28
| 2 | 31, 30, 28 |
| 31, 15, 14 |
∴ So the LCM of the given numbers is 2 x 31 x 15 x 14 = 13020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13020
Therefore, the GCF of Fractions 584/31,506/30,688/28 is 2/13020
Least Common Multiple of 31,30,28 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 31,30,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,30,28) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(31,30,28) x common factors =1 x 2 = 2
LCM(31,30,28) = ( 31 × 30 × 28 ) / 2
LCM(31,30,28) = 26040 / 2
LCM(31,30,28) = 13020
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FAQs on GCF of Fractions of 584/31, 506/30, 688/28
1. What is the HCF of 584,506,688?
The HCF of 584,506,688 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 584/31, 506/30, 688/28?
Answer: GCF of Numerators as per given numbers 584/31, 506/30, 688/28 is
GCF of Numerators i.e. for 584,506,688 is 2
LCM of denominators i.e. for 31,30,28 is 13020.
Thus, GCF of Fractions is 2/13020.Finally, GCF of Fractions for 584/31, 506/30, 688/28 is 2/13020.