GCF of 741/759, 684/676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 741/759, 684/676 i.e 57/513084 easily. The following is the detailed procedure to determine the greatest common factor of fractions 741/759, 684/676.
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 741/759,684/676?
Given fractions are 741/759,684/676
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 741/759,684/676, numerators are 741,684
Denominators are 759,676
The GCF of 741,684 is 57 .
LCM of 759,676 is 513084.
The greatest common factor of 741/759,684/676 = [GCF of 741,684]/[LCM of 759,676]= 57/513084
Therefore, the GCF of 741/759,684/676 is 57/513084.
To find the highest common factor of 741,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 741,684 is 57.
Lets's calculate GCF of 741,684
| 3 | 741, 684 |
| 19 | 247, 228 |
| 13, 12 |
∴ So the GCF of the given numbers is 3 x 19 = 57
Greatest Common Factor of 741,684 By Matching Biggest Common Factor Method
Now, list down the factors of 741
:1,3,13,19,39,57,247,741
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 741,684 . The biggest common factor number is the GCF number.
So the greatest common factor 741,684 is 57.
Lets's calculate LCM of 759,676
Given numbers has no common factors except 1. So, there LCM is their product i.e 513084
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 57/513084
Therefore, the GCF of Fractions 741/759,684/676 is 57/513084
Least Common Multiple of 759,676 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 759,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(759,676) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(759,676) x common factors =1 x 1 = 1
LCM(759,676) = ( 759 × 676 ) / 1
LCM(759,676) = 513084 / 1
LCM(759,676) = 513084
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FAQs on GCF of Fractions of 741/759, 684/676
1. What is the HCF of 741,684?
The HCF of 741,684 is 57
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 741/759, 684/676?
Answer: GCF of Numerators as per given numbers 741/759, 684/676 is
GCF of Numerators i.e. for 741,684 is 57
LCM of denominators i.e. for 759,676 is 513084.
Thus, GCF of Fractions is 57/513084.Finally, GCF of Fractions for 741/759, 684/676 is 57/513084.