GCF of 39/65, 286/78, 624/861
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 39/65, 286/78, 624/861 i.e 13/111930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/65, 286/78, 624/861.
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 39/65,286/78,624/861?
Given fractions are 39/65,286/78,624/861
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 39/65,286/78,624/861, numerators are 39,286,624
Denominators are 65,78,861
The GCF of 39,286,624 is 13 .
LCM of 65,78,861 is 111930.
The greatest common factor of 39/65,286/78,624/861 = [GCF of 39,286,624]/[LCM of 65,78,861]= 13/111930
Therefore, the GCF of 39/65,286/78,624/861 is 13/111930.
To find the highest common factor of 39,286,624, we have to find the factors of both numbers and list the highest common factor.
The factors of 39 are 1, 3, 13, 39
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
The HCF of 39,286,624 is 13.
Lets's calculate GCF of 39,286,624
| 13 | 39, 286, 624 |
| 3, 22, 48 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 39,286,624 By Matching Biggest Common Factor Method
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Now, list down the factors of 624
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Greatest Common Factor
We found the factors 39,286,624 . The biggest common factor number is the GCF number.
So the greatest common factor 39,286,624 is 13.
Lets's calculate LCM of 65,78,861
| 3 | 65, 78, 861 |
| 13 | 65, 26, 287 |
| 5, 2, 287 |
∴ So the LCM of the given numbers is 3 x 13 x 5 x 2 x 287 = 111930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/111930
Therefore, the GCF of Fractions 39/65,286/78,624/861 is 13/111930
Least Common Multiple of 65,78,861 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 65,78,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,78,861) = 1
common factors(in case of two or more numbers have common factors) = 39
GCF(65,78,861) x common factors =1 x 39 = 39
LCM(65,78,861) = ( 65 × 78 × 861 ) / 39
LCM(65,78,861) = 4365270 / 39
LCM(65,78,861) = 111930
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FAQs on GCF of Fractions of 39/65, 286/78, 624/861
1. What is the HCF of 39,286,624?
The HCF of 39,286,624 is 13
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 39/65, 286/78, 624/861?
Answer: GCF of Numerators as per given numbers 39/65, 286/78, 624/861 is
GCF of Numerators i.e. for 39,286,624 is 13
LCM of denominators i.e. for 65,78,861 is 111930.
Thus, GCF of Fractions is 13/111930.Finally, GCF of Fractions for 39/65, 286/78, 624/861 is 13/111930.