GCF of 5920/106, 6700/946
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5920/106, 6700/946 i.e 20/50138 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5920/106, 6700/946.
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 5920/106,6700/946?
Given fractions are 5920/106,6700/946
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 5920/106,6700/946, numerators are 5920,6700
Denominators are 106,946
The GCF of 5920,6700 is 20 .
LCM of 106,946 is 50138.
The greatest common factor of 5920/106,6700/946 = [GCF of 5920,6700]/[LCM of 106,946]= 20/50138
Therefore, the GCF of 5920/106,6700/946 is 20/50138.
To find the highest common factor of 5920,6700, we have to find the factors of both numbers and list the highest common factor.
The factors of 5920 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 37, 40, 74, 80, 148, 160, 185, 296, 370, 592, 740, 1184, 1480, 2960, 5920
The factors of 6700 are 1, 2, 4, 5, 10, 20, 25, 50, 67, 100, 134, 268, 335, 670, 1340, 1675, 3350, 6700
The HCF of 5920,6700 is 20.
Lets's calculate GCF of 5920,6700
| 2 | 5920, 6700 |
| 2 | 2960, 3350 |
| 5 | 1480, 1675 |
| 296, 335 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 5920,6700 By Matching Biggest Common Factor Method
Now, list down the factors of 5920
:1,2,4,5,8,10,16,20,32,37,40,74,80,148,160,185,296,370,592,740,1184,1480,2960,5920
Now, list down the factors of 6700
:1,2,4,5,10,20,25,50,67,100,134,268,335,670,1340,1675,3350,6700
Greatest Common Factor
We found the factors 5920,6700 . The biggest common factor number is the GCF number.
So the greatest common factor 5920,6700 is 20.
Lets's calculate LCM of 106,946
| 2 | 106, 946 |
| 53, 473 |
∴ So the LCM of the given numbers is 2 x 53 x 473 = 50138
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/50138
Therefore, the GCF of Fractions 5920/106,6700/946 is 20/50138
Least Common Multiple of 106,946 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 106,946 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,946) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,946) x common factors =2 x 1 = 2
LCM(106,946) = ( 106 × 946 ) / 2
LCM(106,946) = 100276 / 2
LCM(106,946) = 50138
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FAQs on GCF of Fractions of 5920/106, 6700/946
1. What is the HCF of 5920,6700?
The HCF of 5920,6700 is 20
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 5920/106, 6700/946?
Answer: GCF of Numerators as per given numbers 5920/106, 6700/946 is
GCF of Numerators i.e. for 5920,6700 is 20
LCM of denominators i.e. for 106,946 is 50138.
Thus, GCF of Fractions is 20/50138.Finally, GCF of Fractions for 5920/106, 6700/946 is 20/50138.