GCF of 759/54, 420/697
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 759/54, 420/697 i.e 3/37638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 759/54, 420/697.
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 759/54,420/697?
Given fractions are 759/54,420/697
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 759/54,420/697, numerators are 759,420
Denominators are 54,697
The GCF of 759,420 is 3 .
LCM of 54,697 is 37638.
The greatest common factor of 759/54,420/697 = [GCF of 759,420]/[LCM of 54,697]= 3/37638
Therefore, the GCF of 759/54,420/697 is 3/37638.
To find the highest common factor of 759,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 759,420 is 3.
Lets's calculate GCF of 759,420
| 3 | 759, 420 |
| 253, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 759,420 By Matching Biggest Common Factor Method
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 759,420 . The biggest common factor number is the GCF number.
So the greatest common factor 759,420 is 3.
Lets's calculate LCM of 54,697
Given numbers has no common factors except 1. So, there LCM is their product i.e 37638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/37638
Therefore, the GCF of Fractions 759/54,420/697 is 3/37638
Least Common Multiple of 54,697 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 54,697 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,697) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(54,697) x common factors =1 x 1 = 1
LCM(54,697) = ( 54 × 697 ) / 1
LCM(54,697) = 37638 / 1
LCM(54,697) = 37638
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FAQs on GCF of Fractions of 759/54, 420/697
1. What is the HCF of 759,420?
The HCF of 759,420 is 3
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 759/54, 420/697?
Answer: GCF of Numerators as per given numbers 759/54, 420/697 is
GCF of Numerators i.e. for 759,420 is 3
LCM of denominators i.e. for 54,697 is 37638.
Thus, GCF of Fractions is 3/37638.Finally, GCF of Fractions for 759/54, 420/697 is 3/37638.