GCF of 7000/382, 5928/6709
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7000/382, 5928/6709 i.e 8/2562838 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7000/382, 5928/6709.
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 7000/382,5928/6709?
Given fractions are 7000/382,5928/6709
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 7000/382,5928/6709, numerators are 7000,5928
Denominators are 382,6709
The GCF of 7000,5928 is 8 .
LCM of 382,6709 is 2562838.
The greatest common factor of 7000/382,5928/6709 = [GCF of 7000,5928]/[LCM of 382,6709]= 8/2562838
Therefore, the GCF of 7000/382,5928/6709 is 8/2562838.
To find the highest common factor of 7000,5928, we have to find the factors of both numbers and list the highest common factor.
The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000
The factors of 5928 are 1, 2, 3, 4, 6, 8, 12, 13, 19, 24, 26, 38, 39, 52, 57, 76, 78, 104, 114, 152, 156, 228, 247, 312, 456, 494, 741, 988, 1482, 1976, 2964, 5928
The HCF of 7000,5928 is 8.
Lets's calculate GCF of 7000,5928
| 2 | 7000, 5928 |
| 2 | 3500, 2964 |
| 2 | 1750, 1482 |
| 875, 741 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 7000,5928 By Matching Biggest Common Factor Method
Now, list down the factors of 7000
:1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,125,140,175,200,250,280,350,500,700,875,1000,1400,1750,3500,7000
Now, list down the factors of 5928
:1,2,3,4,6,8,12,13,19,24,26,38,39,52,57,76,78,104,114,152,156,228,247,312,456,494,741,988,1482,1976,2964,5928
Greatest Common Factor
We found the factors 7000,5928 . The biggest common factor number is the GCF number.
So the greatest common factor 7000,5928 is 8.
Lets's calculate LCM of 382,6709
Given numbers has no common factors except 1. So, there LCM is their product i.e 2562838
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/2562838
Therefore, the GCF of Fractions 7000/382,5928/6709 is 8/2562838
Least Common Multiple of 382,6709 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 382,6709 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,6709) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(382,6709) x common factors =1 x 1 = 1
LCM(382,6709) = ( 382 × 6709 ) / 1
LCM(382,6709) = 2562838 / 1
LCM(382,6709) = 2562838
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FAQs on GCF of Fractions of 7000/382, 5928/6709
1. What is the HCF of 7000,5928?
The HCF of 7000,5928 is 8
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 7000/382, 5928/6709?
Answer: GCF of Numerators as per given numbers 7000/382, 5928/6709 is
GCF of Numerators i.e. for 7000,5928 is 8
LCM of denominators i.e. for 382,6709 is 2562838.
Thus, GCF of Fractions is 8/2562838.Finally, GCF of Fractions for 7000/382, 5928/6709 is 8/2562838.