GCF of 504/764, 742/986
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 504/764, 742/986 i.e 14/376652 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/764, 742/986.
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 504/764,742/986?
Given fractions are 504/764,742/986
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 504/764,742/986, numerators are 504,742
Denominators are 764,986
The GCF of 504,742 is 14 .
LCM of 764,986 is 376652.
The greatest common factor of 504/764,742/986 = [GCF of 504,742]/[LCM of 764,986]= 14/376652
Therefore, the GCF of 504/764,742/986 is 14/376652.
To find the highest common factor of 504,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 504,742 is 14.
Lets's calculate GCF of 504,742
| 2 | 504, 742 |
| 7 | 252, 371 |
| 36, 53 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 504,742 By Matching Biggest Common Factor Method
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 504,742 . The biggest common factor number is the GCF number.
So the greatest common factor 504,742 is 14.
Lets's calculate LCM of 764,986
| 2 | 764, 986 |
| 382, 493 |
∴ So the LCM of the given numbers is 2 x 382 x 493 = 376652
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/376652
Therefore, the GCF of Fractions 504/764,742/986 is 14/376652
Least Common Multiple of 764,986 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 764,986 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(764,986) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(764,986) x common factors =2 x 1 = 2
LCM(764,986) = ( 764 × 986 ) / 2
LCM(764,986) = 753304 / 2
LCM(764,986) = 376652
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FAQs on GCF of Fractions of 504/764, 742/986
1. What is the HCF of 504,742?
The HCF of 504,742 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 504/764, 742/986?
Answer: GCF of Numerators as per given numbers 504/764, 742/986 is
GCF of Numerators i.e. for 504,742 is 14
LCM of denominators i.e. for 764,986 is 376652.
Thus, GCF of Fractions is 14/376652.Finally, GCF of Fractions for 504/764, 742/986 is 14/376652.