GCF of 826/54, 742/332
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 826/54, 742/332 i.e 14/8964 easily. The following is the detailed procedure to determine the greatest common factor of fractions 826/54, 742/332.
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 826/54,742/332?
Given fractions are 826/54,742/332
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 826/54,742/332, numerators are 826,742
Denominators are 54,332
The GCF of 826,742 is 14 .
LCM of 54,332 is 8964.
The greatest common factor of 826/54,742/332 = [GCF of 826,742]/[LCM of 54,332]= 14/8964
Therefore, the GCF of 826/54,742/332 is 14/8964.
To find the highest common factor of 826,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 826 are 1, 2, 7, 14, 59, 118, 413, 826
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 826,742 is 14.
Lets's calculate GCF of 826,742
| 2 | 826, 742 |
| 7 | 413, 371 |
| 59, 53 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 826,742 By Matching Biggest Common Factor Method
Now, list down the factors of 826
:1,2,7,14,59,118,413,826
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 826,742 . The biggest common factor number is the GCF number.
So the greatest common factor 826,742 is 14.
Lets's calculate LCM of 54,332
| 2 | 54, 332 |
| 27, 166 |
∴ So the LCM of the given numbers is 2 x 27 x 166 = 8964
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/8964
Therefore, the GCF of Fractions 826/54,742/332 is 14/8964
Least Common Multiple of 54,332 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 54,332 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,332) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,332) x common factors =2 x 1 = 2
LCM(54,332) = ( 54 × 332 ) / 2
LCM(54,332) = 17928 / 2
LCM(54,332) = 8964
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FAQs on GCF of Fractions of 826/54, 742/332
1. What is the HCF of 826,742?
The HCF of 826,742 is 14
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 826/54, 742/332?
Answer: GCF of Numerators as per given numbers 826/54, 742/332 is
GCF of Numerators i.e. for 826,742 is 14
LCM of denominators i.e. for 54,332 is 8964.
Thus, GCF of Fractions is 14/8964.Finally, GCF of Fractions for 826/54, 742/332 is 14/8964.