GCF of 742/65, 782/5668
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 742/65, 782/5668 i.e 2/28340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 742/65, 782/5668.
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 742/65,782/5668?
Given fractions are 742/65,782/5668
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 742/65,782/5668, numerators are 742,782
Denominators are 65,5668
The GCF of 742,782 is 2 .
LCM of 65,5668 is 28340.
The greatest common factor of 742/65,782/5668 = [GCF of 742,782]/[LCM of 65,5668]= 2/28340
Therefore, the GCF of 742/65,782/5668 is 2/28340.
To find the highest common factor of 742,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 742,782 is 2.
Lets's calculate GCF of 742,782
| 2 | 742, 782 |
| 371, 391 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 742,782 By Matching Biggest Common Factor Method
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 742,782 . The biggest common factor number is the GCF number.
So the greatest common factor 742,782 is 2.
Lets's calculate LCM of 65,5668
| 13 | 65, 5668 |
| 5, 436 |
∴ So the LCM of the given numbers is 13 x 5 x 436 = 28340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/28340
Therefore, the GCF of Fractions 742/65,782/5668 is 2/28340
Least Common Multiple of 65,5668 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 65,5668 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,5668) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(65,5668) x common factors =13 x 1 = 13
LCM(65,5668) = ( 65 × 5668 ) / 13
LCM(65,5668) = 368420 / 13
LCM(65,5668) = 28340
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FAQs on GCF of Fractions of 742/65, 782/5668
1. What is the HCF of 742,782?
The HCF of 742,782 is 2
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 742/65, 782/5668?
Answer: GCF of Numerators as per given numbers 742/65, 782/5668 is
GCF of Numerators i.e. for 742,782 is 2
LCM of denominators i.e. for 65,5668 is 28340.
Thus, GCF of Fractions is 2/28340.Finally, GCF of Fractions for 742/65, 782/5668 is 2/28340.