GCF of 858/40, 416/586
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 858/40, 416/586 i.e 26/11720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 858/40, 416/586.
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 858/40,416/586?
Given fractions are 858/40,416/586
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 858/40,416/586, numerators are 858,416
Denominators are 40,586
The GCF of 858,416 is 26 .
LCM of 40,586 is 11720.
The greatest common factor of 858/40,416/586 = [GCF of 858,416]/[LCM of 40,586]= 26/11720
Therefore, the GCF of 858/40,416/586 is 26/11720.
To find the highest common factor of 858,416, we have to find the factors of both numbers and list the highest common factor.
The factors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The HCF of 858,416 is 26.
Lets's calculate GCF of 858,416
| 2 | 858, 416 |
| 13 | 429, 208 |
| 33, 16 |
∴ So the GCF of the given numbers is 2 x 13 = 26
Greatest Common Factor of 858,416 By Matching Biggest Common Factor Method
Now, list down the factors of 858
:1,2,3,6,11,13,22,26,33,39,66,78,143,286,429,858
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Greatest Common Factor
We found the factors 858,416 . The biggest common factor number is the GCF number.
So the greatest common factor 858,416 is 26.
Lets's calculate LCM of 40,586
| 2 | 40, 586 |
| 20, 293 |
∴ So the LCM of the given numbers is 2 x 20 x 293 = 11720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/11720
Therefore, the GCF of Fractions 858/40,416/586 is 26/11720
Least Common Multiple of 40,586 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 40,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,586) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(40,586) x common factors =2 x 1 = 2
LCM(40,586) = ( 40 × 586 ) / 2
LCM(40,586) = 23440 / 2
LCM(40,586) = 11720
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FAQs on GCF of Fractions of 858/40, 416/586
1. What is the HCF of 858,416?
The HCF of 858,416 is 26
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 858/40, 416/586?
Answer: GCF of Numerators as per given numbers 858/40, 416/586 is
GCF of Numerators i.e. for 858,416 is 26
LCM of denominators i.e. for 40,586 is 11720.
Thus, GCF of Fractions is 26/11720.Finally, GCF of Fractions for 858/40, 416/586 is 26/11720.