GCF of 564/362, 8140/946
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 564/362, 8140/946 i.e 4/171226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/362, 8140/946.
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 564/362,8140/946?
Given fractions are 564/362,8140/946
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 564/362,8140/946, numerators are 564,8140
Denominators are 362,946
The GCF of 564,8140 is 4 .
LCM of 362,946 is 171226.
The greatest common factor of 564/362,8140/946 = [GCF of 564,8140]/[LCM of 362,946]= 4/171226
Therefore, the GCF of 564/362,8140/946 is 4/171226.
To find the highest common factor of 564,8140, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 8140 are 1, 2, 4, 5, 10, 11, 20, 22, 37, 44, 55, 74, 110, 148, 185, 220, 370, 407, 740, 814, 1628, 2035, 4070, 8140
The HCF of 564,8140 is 4.
Lets's calculate GCF of 564,8140
| 2 | 564, 8140 |
| 2 | 282, 4070 |
| 141, 2035 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 564,8140 By Matching Biggest Common Factor Method
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 8140
:1,2,4,5,10,11,20,22,37,44,55,74,110,148,185,220,370,407,740,814,1628,2035,4070,8140
Greatest Common Factor
We found the factors 564,8140 . The biggest common factor number is the GCF number.
So the greatest common factor 564,8140 is 4.
Lets's calculate LCM of 362,946
| 2 | 362, 946 |
| 181, 473 |
∴ So the LCM of the given numbers is 2 x 181 x 473 = 171226
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/171226
Therefore, the GCF of Fractions 564/362,8140/946 is 4/171226
Least Common Multiple of 362,946 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 362,946 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(362,946) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(362,946) x common factors =2 x 1 = 2
LCM(362,946) = ( 362 × 946 ) / 2
LCM(362,946) = 342452 / 2
LCM(362,946) = 171226
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 564/362, 8140/946
1. What is the HCF of 564,8140?
The HCF of 564,8140 is 4
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 564/362, 8140/946?
Answer: GCF of Numerators as per given numbers 564/362, 8140/946 is
GCF of Numerators i.e. for 564,8140 is 4
LCM of denominators i.e. for 362,946 is 171226.
Thus, GCF of Fractions is 4/171226.Finally, GCF of Fractions for 564/362, 8140/946 is 4/171226.