GCF of 42/497, 861/235, 819/960
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 42/497, 861/235, 819/960 i.e 21/22424640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/497, 861/235, 819/960.
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 42/497,861/235,819/960?
Given fractions are 42/497,861/235,819/960
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 42/497,861/235,819/960, numerators are 42,861,819
Denominators are 497,235,960
The GCF of 42,861,819 is 21 .
LCM of 497,235,960 is 22424640.
The greatest common factor of 42/497,861/235,819/960 = [GCF of 42,861,819]/[LCM of 497,235,960]= 21/22424640
Therefore, the GCF of 42/497,861/235,819/960 is 21/22424640.
To find the highest common factor of 42,861,819, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The HCF of 42,861,819 is 21.
Lets's calculate GCF of 42,861,819
| 3 | 42, 861, 819 |
| 7 | 14, 287, 273 |
| 2, 41, 39 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 42,861,819 By Matching Biggest Common Factor Method
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Greatest Common Factor
We found the factors 42,861,819 . The biggest common factor number is the GCF number.
So the greatest common factor 42,861,819 is 21.
Lets's calculate LCM of 497,235,960
| 5 | 497, 235, 960 |
| 497, 47, 192 |
∴ So the LCM of the given numbers is 5 x 497 x 47 x 192 = 22424640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/22424640
Therefore, the GCF of Fractions 42/497,861/235,819/960 is 21/22424640
Least Common Multiple of 497,235,960 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 497,235,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(497,235,960) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(497,235,960) x common factors =1 x 5 = 5
LCM(497,235,960) = ( 497 × 235 × 960 ) / 5
LCM(497,235,960) = 112123200 / 5
LCM(497,235,960) = 22424640
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FAQs on GCF of Fractions of 42/497, 861/235, 819/960
1. What is the HCF of 42,861,819?
The HCF of 42,861,819 is 21
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 42/497, 861/235, 819/960?
Answer: GCF of Numerators as per given numbers 42/497, 861/235, 819/960 is
GCF of Numerators i.e. for 42,861,819 is 21
LCM of denominators i.e. for 497,235,960 is 22424640.
Thus, GCF of Fractions is 21/22424640.Finally, GCF of Fractions for 42/497, 861/235, 819/960 is 21/22424640.